p1. an airplane is flying at an altitude of 20,000 ft. what is the local atmospheric pressure at this altitude? what pressure differential would be required to to keep the passengers comfortable? what discomfort might the passengers feel if the cabin pressure drops below this? explain your answer.

The Volumetric efficiency of the pump is the ratio of the actual capacity to the theoretical capacity of the pump.

Volumetric efficiency of the pump = Actual capacity of the pump / Theoretical capacity of the pump

Given Information

The provided information is,

Find

The theoretical capacity of the pump is given by the following formula,

Theoretical capacity of the pump = π/4 x d² x l x n

where:

For the given problem,

We need to find the diameter of the pump and length of the pump to calculate the theoretical capacity of the pump.

Now, we have the actual capacity of the pump.

As we don't have the diameter and length of the pump, it is impossible to calculate the theoretical capacity of the pump.

Hence, the Volumetric efficiency of the pump cannot be calculated.

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Answer:

The reflection of light is the process by which light bounces off a surface and changes direction. When light waves hit a smooth and shiny surface, such as a mirror or a still body of water, the waves bounce back at the same angle as they hit the surface. This is known as the law of reflection. The angle of incidence, which is the angle at which the light waves hit the surface, is equal to the angle of reflection, which is the angle at which the light waves bounce off the surface. The reflection of light plays a crucial role in our daily lives, from the way we see ourselves in the mirror to the way light is directed in optical devices such as telescopes and microscopes.

Explanation:

Answer: When a ray of light approaches a smooth polished surface and the light ray bounces back, it is called the reflection of light.

Explanation:

A reflection is a transformation that acts like a mirror. The best surfaces for reflecting light are very smooth, such as a glass mirror or polished metal.

After the helium flash in a star, the core quickly heats up and expands.

A helium flash is the very brief thermal runaway nuclear fusion of significant amounts of helium into carbon during the red giant phase of low mass stars (between 0.8 solar masses (M) and 2.0 M). The centre expands as a result of the core becoming warmer as a result of this.

Following the onset of helium nuclear reactions in a star's core, helium nuclei fuse to create carbon and oxygen.

Most of the time, the stars' positions in reference to one another remain constant. Convergence between Orion and Taurus is ongoing. Ursa Minor is never far from Draco. The stars appear to us as an endless backdrop painting in the sky that hardly moves in reference to one another.

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The volume of the log is estimated to be 3.225 m3. The total volume of the log is the sum of the volumes of each interval.

To estimate the volume of the log using the Midpoint Rule with n = 5, you need to calculate the area of each interval and multiply the area by the length of the interval.

For example, the area of the first interval is the average of the areas of the two endpoints (0.69 + 0.65)/2 = 0.67 m2. The length of the interval is 1 m, so the volume of this interval is 0.67 m2 x 1 m = 0.67 m3. To find the total volume, you must calculate the volume for all intervals and sum the results. The intervals and the corresponding areas and volumes are listed below:

The total volume of the log is the sum of the volumes of each interval, which is 0.67 m3 + 0.645 m3 + 0.63 m3 + 0.595 m3 + 0.575 m3 = 3.225 m3. Therefore, the volume of the log is estimated to be 3.225 m3.

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The magnitude of the centripetal acceleration (ac) of the car is equal to the tangential acceleration (at) when the car has been accelerating for 1.22 seconds.

The given information is the steady acceleration of the car is 1.5 m/s². We have to find the time taken by the car to reach the magnitude of its centripetal acceleration equal to the tangential acceleration.

Let, v = tangential velocity of the car

a = acceleration of the car

T = time taken by the car to reach the magnitude of its centripetal acceleration equal to the tangential acceleration

Given, the steady acceleration of the car is a = 1.5 m/s²

The centripetal acceleration of the car is given as, ac = v² / r... (i)

We know that the tangential acceleration of the car is a = dv / dt

Where v is the tangential velocity of the car and t is the time taken by the car.

So, dv = a dt Integrating both sides, we get  v = at + cv = at + c... (ii)

At t = 0, v = 0So, c = 0

Putting the value of v in equation (i), we get

ac = (at)² / r... (iii)At t = T, ac = a

Substituting these values in equation (iii), we get

a = (aT)² / raT² = r... (iv)

Hence, the time taken by the car to reach the magnitude of its centripetal acceleration equal to the tangential acceleration is T = √r/a. So, the required time is √r/a = √1.5 m/s² = 1.22 s.

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Answer:

An electric field is essentially a force field that’s created around an electrically charged particle. A magnetic field is one that’s created around a permanent magnetic substance or a moving electrically charged object.

Electric fields are created by electric charges.

Permanent magnets are objects that produce their own persistent magnetic fields.

in electric fields Positive and negative charged objects attract or pull each other together, while similar charged objects (2 positives or 2 negatives) repel or push each other apart

in magnetic fields, Similar magnetic poles repel and unlike magnetic poles attract each other.

Attach a wire running from the negative terminal of the battery to one sheet and a wire running from the positive terminal of the battery to the other sheet

A magnetic field can be created by running electricity through a wire. All magnetic fields are created by moving charged particles. Even the magnet on your fridge is magnetic because it contains electrons that are constantly moving around inside

Answer:

A diameter is also a double of radius

Among the original group of 10,000 stars, approximately 100 stars have planets.

The following data has been given about planetary systems using the transit technique: about 1% of planetary systems can be detected using the transit technique. Imagine that you studied a group of 10,000 stars for many years, watching for them to dip in brightness.

After a long survey, you have discovered 10 planetary systems - stars with planets orbiting them.

The proportion of planetary systems that can be discovered using the transit technique is 1%.The planetary system detected: 10 planets out of 10,000 stars

Among the original group of 10,000 stars, we can estimate that 1% of the stars actually have planets, based on the proportion of the planetary systems that can be detected using the transit technique.

Therefore, the estimated number of stars with planets will be: 1/10 * 10000

= 100

Thus, an estimated 100 stars out of the 10,000 that were observed may have planets.

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The time taken to fill the bucket with a garden hose attached with a nozzle of inner diameter of 1 in and  reduces to 0.4 in at the nozzle exit is 0.010268347 seconds.

Formula used:Q = AV Where Q is the volume of water, A is the area of the hose, and V is the velocity of water.Substituting the given values,

Volume of the bucket= 20 gal× 3.7854 L/ gal = 75.708 L= 75.708000 cm³

Diameter of the hose = 1 in = 2.54 cm.

Radius of hose at entry = d/2 = 2.54/2 cm. Radius of hose at nozzle exit = d/2 = 0.4/2 cm.

Velocity of water = 6 ft/s = 182.88 cm/s.

Area of hose at entry = πr² = π(1.27)² cm² = 5.07 cm².Area of hose at nozzle exit = πr² = π(0.2)² cm² = 0.1257 cm²

Initial volume of water = 0 (since there is no water initially in the bucket).Let t be the time taken to fill the bucket.Q1 = A1V1t1 = 5.07 cm² × 182.88 cm/s × tVolume of water after time t = Q1 = 5.07 × 182.88t cm³.Let us determine the cross-sectional area of the nozzle.A2 = πr² = π (0.2)² cm² = 0.1257 cm²

Now, we can determine the volume of water that comes out in time, t.Q2 = A2V2t2 = 0.1257 × V2 × tThe volume of water that comes out in time t = Q2 = 0.1257 × V2 × t.Let the density of water be ρ.Substituting the values,Q1 = Q2∴5.07 × 182.88t = 0.1257 × V2 × tV2 = 5.07 × 182.88/0.1257= 7376.376 cm³/s.Let the mass of water flowing out per second be m.V2 = A2v2= πr²v2= 0.1257 v2m/ρ = A1V1= 5.07 cm² × 182.88 cm/sm/ρ = 5.07 × 182.88/0.1257m = 6.112 g/s

The mass of water flowing out per second is 6.112 g/s.The time required to fill the bucket can be calculated as follows.Total volume of water to be filled in the bucket = 75.708000 cm³Time taken to fill the bucket, t = (Total volume of water to be filled in the bucket)/Volume of water filled in 1 second t = 75.708000 cm³/7376.376 cm³/st = 0.010268347 s. Therefore, the time taken to fill the bucket is 0.010268347 seconds.

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(a) Yes, an electric field can exert a force on a stationary charged object. A stationary charged object will experience a force in the direction of the electric field due to the Coulombic interaction between the charges.

(b) No, a magnetic field does not exert a force on a stationary charged object. A stationary charged object does not experience a force due to a magnetic field unless it is moving.

(c) Yes, an electric field can exert a force on a moving charged object. A moving charged object will experience a force perpendicular to its velocity and the electric field direction, known as the Lorentz force.

(d) Yes, a magnetic field can exert a force on a moving charged object. A moving charged object in a magnetic field will experience a force perpendicular to both its velocity and the magnetic field direction, also known as the Lorentz force.

(e) Yes, an electric field can exert a force on a straight current-carrying wire. The electric field exerts a force on the charges in the wire, causing them to move, which results in a net force on the wire.

(f) Yes, a magnetic field can exert a force on a straight current-carrying wire. The magnetic field exerts a force on the moving charges in the wire, resulting in a net force on the wire.

(g) Yes, an electric field can exert a force on a beam of moving electrons. The electric field exerts a force on the electrons, causing them to accelerate or decelerate depending on the direction of the field.

(h) Yes, a magnetic field can exert a force on a beam of moving electrons. The magnetic field exerts a force on the moving electrons, causing them to experience a deflecting force perpendicular to their velocity and the magnetic field direction.

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Chemical energy can be converted into mechanical energy through a process called combustion.

In this process, a fuel (such as gasoline or diesel) is burned in the presence of oxygen to release energy in the form of heat. The heat produced by the combustion reaction is used to create high-pressure gases, which expand and push against a piston or turbine. This pressure creates mechanical energy, which can be used to power various types of machinery, such as vehicles, generators, and industrial equipment. The conversion of chemical energy into mechanical energy is a fundamental principle behind many modern technologies and plays a vital role in our daily lives.

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The best example that shows the potential energy is a body at rest from some height from the ground, thus the correct answer is option b.

Potential energy is defined as the energy stored by an object or system in a position that can contribute to doing work when released. It is the stored energy of an object or system.

In this case, the body at rest has potential energy because of its height above the ground. As it falls, the potential energy is converted to kinetic energy.

Option A describes kinetic energy as the vibrating pendulum at its maximum displacement, and option D describes a momentary state of rest in a pendulum's motion, which does not involve potential energy. Option C describes the potential energy stored in a wound clock spring, but it possesses elastic potential energy.

Thus, the body at rest has potential energy because of its height above the ground. Thus, option b is correct.

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An electron must absorb a photon of energy in order to go up an atom's levels. The electron gains energy as a result and jumps to a higher energy level.

An electron in an atom must absorb a photon of energy equal to the energy difference between the two levels in order to go from one level of energy to another. Excitation is the term for this action. The electron is elevated to a higher energy level after absorbing the photon. The electron will swiftly revert to its initial energy level, producing a photon with an energy equal to the difference between the two levels, as this is an unstable condition. A photon is released as a result of this procedure, which is also known as de-excitation or relaxation. Instruments that can detect this photon can be used to examine the energy levels of atoms.

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The direction of the force on the charge due to the magnetic field is given by option B, which says that vector F points into the page

For each of the situations below, a charged particle Part B enters a region of uniform magnetic field. Determine the direction of the force on each charge due to the magnetic field.

The direction of the force on the charge due to the magnetic field is given by option B, which says that vector F points into the page. Hence, option B is the correct answer.

The Lorentz force is the force experienced by a charged particle in an electromagnetic field. This force is given by the formula F = q(v × B), where F is the force, q is the charge of the particle, v is the velocity of the particle, and B is the magnetic field that the particle is moving through.

This equation applies only to situations where the magnetic field is constant and the velocity of the charged particle is perpendicular to the magnetic field.

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The distance d so that the vertical reaction under the front wheels (point b) is 300lb due to the three force is equal to 200 ft. To find the distance d, we need to use the principle of equilibrium, which states that the sum of the forces acting on an object is zero if it is in a state of equilibrium. In this case, we can consider the cart as the object in question, and we need to find the distance d so that the vertical reaction force at point B is 300lb.

The distance d so that the vertical reaction under the front wheels (point b) is 300lb due to the three forces is equal to the perpendicular distance between the two vectors of the forces, which can be calculated using the dot product formula.


The dot product of two vectors can be calculated using the formula:

d = ((F1x × F2x) + (F1y × F2y))/|F2|


Where F1 and F2 are the two forces, F1x and F1y are the x and y components of F1, and F2x and F2y are the x and y components of F2. |F2| is the magnitude of F2.


By plugging in the x and y components of the forces, we can calculate the distance d:

d = ((-50 × 200) + (400 × 300))/500 = 200 ft


Therefore, the distance d so that the vertical reaction under the front wheels (point b) is 300lb due to the three forces is equal to 200 ft.

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The distance which the football which cover before landing back on the ground level will be about 56.4 meters.

The mass of football, m = 0.43 kg, Initial velocity of football (v) = 24 m/s, Angle of inclination(θ) = 53°

From the given data, we know that the vertical component of the initial velocity is given by, vsin(θ) and the horizontal component of initial velocity is given by, vcos(θ). So, the time taken by the football to reach the maximum height is given by,

t = (vsin(θ))/g

Here, g = 9.8 m/s²

Now, the maximum height attained by the football is given by,h = (vsin(θ))²/(2g).

Therefore, the time of flight or the total time which is taken by the football to land on the ground level is given by,

T = 2t

Now, the horizontal distance travelled by the ball is given by, d = (vcos(θ))T

Substituting the given values in the above formulas, we get:

t = (24sin(53°))/9.8 = 1.71 s

h = (24sin(53°))²/(2×9.8) = 23.4m

T = 2×1.71 = 3.42 s

d = (24×cos(53°))×3.42 = 56.4 m

Therefore, the football will go 56.4 m before it is landing back on the level ground.

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The ratio of the orbital period of planet B to that of planet A is T_B/T_A = Squareroot 8.

A planet is an astronomical object that orbits a star and does not produce its own light. The vast majority of the thousands of objects we call planets orbit a star in our Solar System. This specific system includes the sun and the eight planets that orbit around it.

Two planets A and B, where B has twice the mass of A, orbit the Sun in circular orbits. The radius of the circular orbit of planet B is two times the radius of the circular orbit of planet A. The formula for calculating the time period of a circular orbit is:

T = (2πr) / v

where, r = radius, v = velocity

For circular orbits, T ∝ (r³/²)

Therefore, T_B/T_A = (r_B³/²) / (r_A³/²)T_B/T_A = (2³/²) / 1³/2T_B/T_A = (square root 8)/1T_B/T_A = Squareroot 8.

Therefore, the ratio of the orbital period of planet B to that of planet A is T_B/T_A = Squareroot 8.

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Answer:

Light energy

Explanation:

When an electron releases or absorbs energy, it goes into an "exited state" which means it goes into a lower or higher energy level respectively. This will radiate light energy.

The maximum length of the spring (Lmax) is about 1.25 meters.

To calculate the maximum length of the spring during the motion that follows, we can use the following equation:

Lmax = L₀ + (mv²) / (2k)

where L₀ is the unstretched length of the spring, m is the mass of the object, v is the initial velocity, and k is the spring constant. In this case, L₀ = 0.42 m, m = 0.3 kg, v = 1.2 m/s, and k = 39 N/m.

The maximum length of the spring is:

Lmax = 0.42 + (0.3 × (1.2)²) / (2 × 39) = 1.25 meters

Therefore, the maximum length of the spring during motion is 1.25 meters.

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By keeping their centre of gravity over the beam, a gymnast may balance himself. The gymnast increases their moment of inertia, or resistance to rotational motion, by spreading their arms out to the sides, making it harder to unintentionally tilt or spin. As a result, their body is more stable, aiding in balance maintenance. Moreover, the centre of mass can be slightly adjusted with the arm movements to make up for any minor deviations from the equilibrium position. The gymnast can also orient oneself in relation to the beam using the visual clues provided by the arms. Overall, while balancing on a beam, a gymnast can gain various advantages from extending their arms to the side, including increased stability and many more.

At the shop, Joselyn purchased 2700 grammes of salt water taffy.

To convert kilograms (kg) to grams (g), Joselyn would need to multiply the weight in kilograms by 1000. This is because there are 1000 grams in 1 kilogram. Therefore, to find out how many grams of salt water taffy Joselyn bought, she would need to multiply 2.7kg by 1000.

The correct answer is (B) Multiply by 1000.

Multiplying 2.7kg by 1000 gives:

2.7kg x 1000 = 2700g

So Joselyn bought 2700 grams of salt water taffy at the store.

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The HST speed ratio is: 19.29:1.

A hydrostatic transmission has a pump displacement of 1 cir and a motor displacement of 19 cir.

The volumetric efficiency of the pump is 94 % and the volumetric efficiency of the motor is 94 %. The mechanical efficiency of the pump is 95 % and the mechanical efficiency of the motor is 93 %.

Hydrostatic transmission (HST) comprises of a hydraulic pump with a variable displacement capacity and a hydraulic motor with a fixed displacement capacity. HST consists of a hydraulic circuit that comprises of a pump, motor, pipes, hoses, hydraulic fluid, and regulators. They are frequently used in construction equipment like bulldozers and excavators.

HST Speed Ratio Calculation Speed ratio for the hydrostatic transmission (HST) can be calculated by the formula below: Speed Ratio = (Motor Displacement/Pump Displacement) x (Efficiency of the Pump/Efficiency of the Motor)

Here, Motor Displacement = 19 cir

Pump Displacement = 1 cir

Efficiency of the Pump = 94%

Mechanical Efficiency of the Motor = 93%

Putting the values in the formula, we get; Speed Ratio = (19/1) x (0.94/0.93) = 19.29:1

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A kangaroo jumps straight up to a vertical height of 1.45 m. The time the kangaroo was in the air before returning to the ground was 0.5304 seconds. The given data can be used to calculate the time the kangaroo was in the air before returning to the ground.

The initial velocity of the kangaroo is zero since it was at rest, and it jumps straight up to a height of 1.45 m from the ground.

Using the formula for vertical motion,

vf = u + gt,

where

We can substitute these values and gett = 0.5304 seconds

Therefore, the kangaroo was in the air for 0.5304 seconds.

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The orbital speed of the second satellite is 6.55 × 10³ m/s.

The formula used to find the orbital speed of a satellite is given as v=√(GM/r).

Therefore, the value of the first satellite's speed is given as v₁=1.89×104 m/s, and the radius is r₁=2.76×106 m. Using the above formula, the mass of the planet is given as:

M= v²r/G= (1.89×104 m/s)² (2.76×106 m)/(6.6743 × 10⁻¹¹ Nm²/kg²) = 5.31 × 10²⁴ kg.

Now, the orbital speed of the second satellite, given as v₂, is equal to:

v₂ = √(GM/r₂); where G = gravitational constant = 6.6743 × 10⁻¹¹ Nm²/kg²;

M = mass of the planet = 5.31 × 10²⁴ kg;

r₂ = radius of orbit of the second satellite = 6.98 × 10⁶ m.

Substituting the values given above, we get:

v₂ = √(GM/r₂)= √[(6.6743 × 10⁻¹¹ Nm²/kg²) × (5.31 × 10²⁴ kg) / (6.98 × 10⁶ m)] = 6.55 × 10³ m/s

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At 27 degrees Celsius, the rms speed of nitrogen molecules is roughly 515 m/s, which is faster than the sound speed in air.

The square root of the average of the square of the velocity is the root mean square velocity. It has velocity units as a result. As the particles in a typical gas sample are flowing in all directions, the average velocity for that sample is zero, which is why we use the rms velocity instead of the average.

The following formula determines a gas molecule's root mean square (rms) speed: v(rms) = √(3kT/m)

where T is the temperature in Kelvin, m is the molar mass of the gas in kg/mol, and k is Boltzmann's constant (1.38 10-23 J/K).

We must change the molar mass from g/mol to kg/mol in order to determine the rms speed of nitrogen molecules at 27 °C (300 °F):

m = 28.0 g/mol / 1000 g/kg = 0.028 kg/mol

Now we can plug in the values and solve for v(rms):

v(rms) = √(3kT/m)

v(rms) = √(3 × 1.38 × 10^-23 J/K × 300 K / 0.028 kg/mol)

v(rms) = 515 m/s (rounded to three significant figures)

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The wavelength of the laser is 0.4464 mm.

The equation for the diffraction grating is given as:

dsinθ = mλ

where d is the distance between the slits (in meters), θ is the angle between the central maximum and the mth bright fringe (in radians), m is the order of the bright fringe, and λ is the wavelength of the light (in meters).

The equation to calculate the wavelength of a laser is λ = d × sin θ/m, where d is the distance between two adjacent slits on the diffraction grating (in this case, 1000 slits/mm, which is equivalent to 1 mm), θ is the angle of the fringe relative to the central axis (in this case, 26 degrees), and m is the order of the fringe (in this case, m=1). Therefore, plugging in the values:

λ = 1 mm × sin 26°/1 = 0.4464 mm

The wavelength of the laser is 0.4464 mm.

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Molly's experiment involved kicking a soccer ball with varying amounts of force and observing the resulting change in the ball's motion.

Newton's three laws of motion can help explain how the force of Molly's kicks affected the ball's movement.

Newton's first law of motion states that an object at rest will stay at rest and an object in motion will stay in motion with a constant velocity unless acted upon by an unbalanced force. In this experiment, the soccer ball was at rest before each kick, so the force of Molly's kicks acted as an unbalanced force, causing the ball to accelerate and move. The greater the force of her kick, the greater the acceleration and resulting distance the ball traveled.

Newton's second law of motion states that the acceleration of an object is directly proportional to the force applied and inversely proportional to its mass. In this case, the mass of the soccer ball remained constant, but the force of Molly's kicks varied. As a result, the acceleration of the ball was directly proportional to the force of her kick.

Finally, Newton's third law of motion states that for every action, there is an equal and opposite reaction. When Molly kicked the soccer ball, the ball exerted an equal and opposite force back on her foot, which is why she felt the impact of the kick.

Energy transfer also played a role in this experiment. When Molly kicked the ball, she transferred energy from her foot to the ball. The greater the force of her kick, the more energy was transferred to the ball, resulting in a greater distance traveled.

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The mass of the other star in a binary system is 0.14 solar masses.

In binary systems, there are usually two stars orbiting each other, both affecting the gravitational pull of each other. According to Kepler’s laws of planetary motion, the square of the period of revolution is directly proportional to the cube of the semi-major axis of the ellipse traced by the planet/satellite.

So, using the above formula, we get:

T² = 4π²a³/G(M + m)

where, M = mass of 1st star and m = mass of 2nd star.

Using given values, we have:

55.4² = 4π² (24.2)³/G(0.7 + m)

m = 0.14 solar masses

Therefore, the other star in a binary system has a mass of 0.14 solar masses.

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The amount of heat required to raise a 2.0 kg piece of copper from [tex]20^\circ C[/tex] to [tex]250^\circ C[/tex] using the formula [tex]c = \alpha + \beta T + \delta T^{-2}[/tex] is  [tex]1.96 \times 10^{8} J[/tex].

The formula for computing the amount of heat that is required to raise the temperature of an object is expressed as:
Q = mc∆T
Where:
Q: the amount of heat needed in joules
m: the mass of the substance in kilograms
c: the specific heat capacity of the substance in joules per kilogram per kelvin
∆T: the change in temperature in kelvin

We can use the equation to calculate the amount of heat needed to raise the temperature of a 2.00-kg piece of copper from 20∘C to 250∘C. However, it's important to note that we need to first convert the given temperatures from Celsius to Kelvin.

[tex]20^\circ C + 273 = 293 K[/tex] (Initial temperature)

[tex]250^\circ C + 273 = 523 \ K[/tex] (Final temperature)

We can now substitute the values into the formula, Q = mc∆T to get the amount of heat required.

[tex]Q = mc\Delta T[/tex]

[tex]Q = (2.00 \ kg) (\alpha + \beta T + \delta T^{-2}) (\Delta T)[/tex]

[tex]Q = 2.00 kg (\alpha\Delta T + \beta \Delta T^2 + \delta \Delta T^3)[/tex]

[tex]Q = 2.00 kg [(\alpha(523 \ K - 293 \ K) + \beta (523 K^2 - 293\ K^2) + \delta(523 \ K^3 - 293 \ K^3)][/tex]

[tex]Q=2.00 kg [(349 J/kgK \times 230\ K) + (0.107 J/kgK^2 \times 230 K^2) + (4.58 \times 10^5 JkgK \times 230 K^3)][/tex]

[tex]Q = 2.00\ kg [80270\ J + 24.61\ J + 9.8 \times 10^{7} \ J][/tex]
[tex]Q = 1.96 \times 10^{8} J[/tex]
Therefore, the amount of heat that is required to raise a 2.00-kg piece of copper from [tex]20^\circ C[/tex] to 250° C is [tex]1.96 \times 10^{8} J[/tex].

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a) The distribution of X: X-N(129.77,2.26),

b) the proportion of her laps that are completed between 131.69 and 134.04 seconds 0.1670,

c) the fastest 4% of laps are under 126.1965 seconds,

d) the middle 70% of her laps are from seconds 127.5323 to 131.0277 seconds.

a. The distribution of X is the normal distribution with a mean of 129.77 seconds and a standard deviation of 2.26 seconds. Therefore, the distribution of X is X - N(129.77, 2.26).

b. The area between 131.69 and 134.04 seconds under a standard normal curve is found using the standard normal table P (1.05) = 0.8531P (1.71) = 0.9564

Therefore, the proportion of laps completed between 131.69 and 134.04 seconds is

P(131.69 ≤ X ≤ 134.04) = P[(131.69 - 129.77)/2.26 ≤ Z ≤ (134.04 - 129.77)/2.26]

= P(0.8496 ≤ Z ≤ 1.8814) = P(Z ≤ 1.8814) - P(Z ≤ 0.8496)

= 0.9693 - 0.8023

= 0.1670

Therefore, the proportion of laps that are completed between 131.69 and 134.04 seconds is 0.1670.

c. The value corresponding to the lowest 4% is found: P (z) = 0.04. The value of z corresponding to the lowest 4% is obtained as follows:

z = P−1(0.04) = -1.7507

So, the number of seconds that the fastest 4% of laps are under is:

x = μ + zσ = 129.77 - (1.7507)(2.26)

= 126.1965

Therefore, the fastest 4% of laps are under 126.1965 seconds.

d. We know that z corresponding to the lowest 15% is -1.036 and that z corresponding to the highest 15% is 1.036.

Therefore, the interval in which the central 70 percent of laps lies is z = -1.036, 1.036

z = P(X) - P(X) = P(z ≤ X) - P(z ≤ X) = P(z ≤ -1.036) - P(z ≤ 1.036)

= 0.1492 - 0.8513

= -0.7021

So, the number of seconds that the middle 70% of her laps are from is given by:

x = μ + zσ = 129.77 + (-0.7021)(2.26) = 127.5323 and

x = μ + zσ = 129.77 + (0.7021)(2.26) = 131.0277

Therefore, the middle 70% of her laps are from seconds 127.5323 to 131.0277 seconds.

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