How do we know sampling distribution is normal? Sample proportions and sample means

a) The 22nd percentile for incubation times of chicken eggs is of: 20.5 days.

b) The middle 95% of incubation times is in this following interval: (19.1, 23.5) days.

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The parameters for this problem are given as follows:

[tex]\mu = 21.3, \sigma = 1.1[/tex]

The 22nd percentile is the value of X when Z has a p-value of 0.22, hence X when Z = -0.77, thus:

-0.77 = (X - 21.3)/1.1

X - 21.3 = -0.77 x 1.1

X = 20.5 days.

The middle 95% of incubation times is obtained from X when Z = -1.96(2.5th percentile) to X when Z = 1.96(97.5th percentile), hence:

-1.96 = (X - 21.3)/1.1

X - 21.3 = -1.96 x 1.1

X = 19.1 days.

1.96 = (X - 21.3)/1.1

X - 21.3 = 1.96 x 1.1

X = 23.5 days.

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a) The ratio of red to blue marbles is 1:2.

b) The ratio of white to red marbles is 3:2.

c)  The probability of drawing a white marble from the bag is 33%.

The ratio is the relative size of a value compared to another.

Ratios show the quantity of one variable contained in a larger variable.

On the other hand, the probability is the odds or likelihood that an expected outcome occurs given many possible outcomes.

Both ratios and probabilities can be expressed in fractions, decimals, and percentages because they are fractional values.

The number of red marbles in the bag = 20

The number of white marbles in the bag = 30

The number of blue marbles in the bag = 40

The total number of marbles in the bag = 90

a) The ratio of red to blue marbles = 20:40 = 1:2

b) The ratio of white to red marbles = 30:20 = 3:2

The sum of ratios of all marbles = 9 (2:3:4)

c) The probability of drawing a white marble from the bag = 3/9  = 0.33 or 33%

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Answer:

Graphed line is shown below

Step-by-step explanation:

m = 1/3, (-3, 3)

y - y1 = m (x - x1)

y - 3 = 1/3 (x + 3)

y - 3 = (1/3)x + 1

y = (1/3)x + 4

Answer:

B

Step-by-step explanation:

if a polynomial f(x) is divisible by (x - a) , then f(a) = 0

for the polynomial to be divisible by (x - 3) then the polynomial will equal zero when x = 3 , that is

3³ - 9(3)² + 3n - 12 = 0

27 - 9(9) + 3n - 12 = 0

27 - 81 + 3n - 12 = 0

3n - 66 = 0 ( add 66 to both sides )

3n = 66 ( divide both sides by 3 )

n = 22

The area of the region bounded by the three lines is 4.

The region bounded by the three lines y = 0, y = x and y = 2x is a triangle. To find the area of this region, we need to split the integral into two parts. The first part is the area of the triangle formed by y = 0, y = x and y = 2x. This can be found by integrating y from 0 to x, and x from 0 to 2x. The second part is the area of the triangle formed by y = 0, y = x and y = 0. This can be found by integrating y from 0 to x, and x from 0 to 0.

Therefore, the area of the region bounded by the three lines is given by:

[tex]A = 1/2 ∫x=0 to 2x ∫y=0 to x dy dx + 1/2 ∫x=0 to 0 ∫y=0 to x dy dxA = 1/2[x^2/2]_0^2x + 1/2[x^2/2]_0^0\\A = x^2 \\A = 4[/tex]

The area of the region bounded by the three lines is 4.

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One way to figure out the fairness of the coin is to conduct a large number of coin flips and record the number of heads and tails.

Probability is a measure of the likelihood of an event occurring. In the context of a coin flip, the probability of an event is the ratio of the number of favorable outcomes to the total number of possible outcomes.

For a fair coin, the two possible outcomes are heads (H) and tails (T). The probability of getting heads or tails in a single coin flip is equal to 1/2, or 50%. This means that if you flip a fair coin 100 times, you would expect to get approximately 50 heads and 50 tails.

It's important to note that probability is a theoretical concept, and the actual outcome of a coin flip can never be predicted with 100% certainty. However, the law of large numbers states that as the number of coin flips increases, the ratio of heads to tails will approach the theoretical probability.

The concept of probability can also be applied to more complex events involving multiple coin flips. For example, the probability of getting two heads in a row is (1/2) * (1/2) = 1/4, or 25%. The probability of any specific sequence of heads and tails can be calculated using the same method.

One way to figure out the fairness of the coin is to conduct a large number of coin flips and record the number of heads and tails. Then, calculate the proportion of heads and compare it to 0.5, which is the expected proportion for a fair coin. The larger the sample size, the more confident you can be in your conclusion about the fairness of the coin. If the proportion of heads is close to 0.5, it is likely that the coin is fair. If the proportion deviates significantly from 0.5, it is likely that the coin is not fair. It's also important to use a rigorous statistical method to test the hypothesis of fairness, such as a one-sample proportion test, to account for random fluctuations in the results.

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A excel spreadsheet computes likelihood of various upsides of objectives scored in a game utilizing the POISSON.DIST capability. The equation for x=2, 5 and x>3 objectives is given.

In the Succeed calculation sheet, Segment A rundowns the various upsides of x that we need to track down the probabilities for.

Segment B contains the relating equation to ascertain the likelihood utilizing the POISSON.DIST capability.

The recipe in cell B1 works out the likelihood of scoring 2 objectives in a game, P(x = 2), utilizing the POISSON.DIST capability with the contentions 2, 3.3, and Misleading.

The equation in cell B2 computes the likelihood of scoring 5 objectives in a game, P(x = 5), utilizing the POISSON.DIST capability with the contentions 5, 3.3, and Misleading.

The recipe in cell B3 works out the likelihood of scoring multiple objectives in a game, P(x > 3), utilizing the POISSON.DIST capability with the contentions 3, 3.3, and Valid. The Genuine contention works out the combined conveyance capability, which gives the likelihood of getting a worth not exactly or equivalent to the contention. To track down the likelihood of getting a worth more prominent than the contention, deduct the combined dissemination capability from 1.

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Angle of triangle AFC is 37°

An angle is the formed when two lines meet at the same vertex. It is measured is degrees. There are three types of angles based on their measurements.

From the given figure consider ABCF as trapezium,

Given that angle of triangle BCF is 37°

Two pairs of adjacent angles of a trapezium formed between the parallel sides and one of the non-parallel side, add up to 180°

Therefore, ∠BCF + ∠CBF = 180°

                                  ⇒∠B = 180° - 37°⇒143°

Similarly ∠A = ∠B = 143°

⇒∠A+∠F=180°

⇒∠F=180°-143° ⇒ 37°

Hence, m∠AFC = 37°.

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The point (-5,-3) reflected over the y-axis is (5, -3).

There are two ways of reflection.

Along x-axis:

(x, y) – (x, -y)

Along y-axis:

(x, y) - (-x, y)

We have,

(-5, -3)

Along y-axis:

(x, y) → (-x, y)

So,

(-5, -3) → (-(-5), -3) = (5, -3)

Thus,

(5, -3) is the reflected point.

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[tex]\begin{cases} x = -2 &\implies x +2=0\\ x = 5 &\implies x -5=0\\ \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{original~polynomial}{a ( x +2 )( x -5 ) = \stackrel{0}{y}}\hspace{5em}\stackrel{\textit{since the leading coefficient is 2, let's a = 2}}{2(x+2)(x-5)=y} \\\\\\ 2\stackrel{\textit{F O I L}}{(x^2-3x-10)=y}\implies \boxed{2x^2-6x-20=y}[/tex]

Answer: The polynomial P(x) = x³ + 3x² - 2x + 4 is a cubic polynomial with the following properties:

p2 = 2: the coefficient of the x² term in P(x)

p - 2 = -2: the constant term in P(x)

p0 = 4: the coefficient of the x³ term in P(x)

So, p2 = 2, p - 2 = -2, and p0 = 4.

Step-by-step explanation:

Answer:

-18 - x = 107

Step-by-step explanation:

Answer:

Step-by-step explanation:

The wooden frame is a cuboid

and the volume of a cuboid = Length x Width x Depth

Therefore,

The volume of this wooden frame = (8 feet) x (5 feet) x (4 feet)

                                                         = 160 cubic feet

The purchasing rate for the sand is $20 per cubic meter (which is NOT the same as cubic feet)

Unit conversion has to be applied then:

1 foot = 0.3048 meters

1 cubic feet = (0.3048 meters) x (0.3048 meters) x (0.3048 meters)

                                           1 cubic feet = [tex]0.3048^{3}[/tex] cubic meters

Therefore:                     160 cubic feet = (160)([tex]0.3048^{3}[/tex]) cubic meters

                                                                 Cost of sand:
                                                          1 cubic meter = $20

     Therefore:             (160)([tex]0.3048^{3}[/tex]) cubic meters = $(20)(160)([tex]0.3048^{3}[/tex])

                                                                                = $90.61

                                                           = $91 (Rounded to the nearest dollar)

It will cost Andrea $91 to purchase sand for the sandbox

According to the histogram 87.5 - 90.5 range of length (in inches) contains the longest sampled eastern diamondback rattlesnake.

In statistics, a histogram is a graphic representation of data distribution. Each bar in the histogram represents a different type of data, and the histogram is displayed as a group of adjacent rectangles. Statistics is a discipline of mathematics that is used in many different fields.

Frequency, which may be expressed as a table and is known as a frequency distribution, is the repeating of numbers in statistical data. One type of graph that can be used to illustrate a frequency distribution visually is a histogram.

The range of a histogram is the x-axis breadth that the bars cover. Since histograms show bin values rather than actual data values, these numbers are approximations.

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Complete question:

Question According to the histogram, which range of length (in inches) contains the longest sampled Eastern diamondback rattlesnake? Provide your answer below: greater than but less than

Among Tony, Hans and Dante, Dante made flyers the fastest and he took least time to do the work of making flyers.

Time and work deals with the time it takes an individual or group to complete a task and the efficiency of the work they do. 

According to the information given in the question:

Tony made 8 flyers in 64 minutes

Hans made 3 flyers in 21 minutes

Dante made 6 flyers in 30 minutes

By observing, it says

Tony took 8 minutes to make 1 flyer

Hans took 7 minutes to make 1 flyer

Dante took 5 minutes to make 1 flyer

Hence, it can be concluded by time and work relationship that Dante was the fastest among the three competitors.

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C. An IQ score of 80 is more unusual than an IQ score of 120

is the false answer

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.

here, we have,

Firstly we need to find the probability of the test score to be less than 90(P<90) then we will continue finding the probability of the IQ score to be between 90 and 110(90<P<110) then we find the probability of the IQ score being more than 110 (P>110).

For P<90

Firstly we compute this using a scientific calculator where we choose the stat option and enter the mean of 100 and a standard deviation of 10, so we check if we make the normal random variable(X) to be 90 the outcome or answer for that is 0.16 so now we know the probability of the IQ score to be less than 90 is 16% chances.

For 90<P<110

then we check with the same method what will be the probability for an IQ score to be between 90 and 110 for a mean of 100 and a standard deviation of 10 we again check a normal  random variable(X) of 110 to see what will be the probability of P<110 which we find an answer of 0.84 which is 84% chances so now therefore the probability of an IQ score to be more than 110 is 0.

therefore this tells us an IQ score of 120 is more unusual than an IQ score of 120.

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Answer:

5

Step-by-step explanation:

First we do the equation in parathesis

4 - 3 = 1

Now we add 4.

1 + 4 = 5

Answer:

5

Step-by-step explanation:

(x - 3) + 4

(4 - 3) + 4

1 + 4

5

The degree of this polynomial is 4.

What is the polynomial?

A polynomial is an algebraic expression consisting of variables and coefficients, combined using only addition, subtraction, and multiplication. Polynomials can have constants (numbers), variables (letters), and exponents (powers). A polynomial is named after the degree of its highest-degree term, with the degree being the exponent of the variable.

The degree of a polynomial is the highest exponent in the polynomial. In this case, the polynomial is "K4," which has only one term.

The degree of this polynomial is 4.

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9.03 divided by 0.15 is equal to 60.2.

The opposite of multiplication in arithmetic is called division. It's used to determine how many times one quantity is contained inside another. Division is done by dividing the dividend by the divisor, which can be done visually by using the division sign () or a fraction bar (/). The quotient, which shows how many times the dividend can be divided by the divisor, is the operation's output. For instance, if you split up eight apples into four equally sized pieces, each piece would contain two apples. This division is denoted by the equation 8/4 = 2, where 8 is the dividend, 4 is the divisor, and 2 is the quotient.

The division of 9.03 by 0.15 can be calculated as follows:

9.03 ÷ 0.15 = 9.03 / 0.15

= 60.2

So, 9.03 divided by 0.15 is equal to 60.2.

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Answer:

34

Step-by-step explanation:

4r² + 3s² - rs ← substitute r = - 1, s = 3 into the expression

= 4(- 1)² + 3(3)² - (- 1)(3)

= 4(1) + 3(9) - (- 3)

= 4 + 27 + 3

= 34

Using the drop-down menu below to write an inequality is V ≥ 10. The number of visits she needs to make in order to get a free movie ticket is 10.

We have,

75 rewards points just for signing up.

earns 13.5 points for each visit to the movie theater

she needs at least 210 points for a free movie ticket

To write the inequality representing v is,

75 + 13.5v ≥  210

13.5v ≥ 210 - 75

13.5 v ≥ 135

v ≥ 10

Therefore, by solving inequality  the number of visits she needs to make in order to get a free movie ticket is 10.

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The Formula is [tex]a_n[/tex]= 50 ([tex]2^{n-1[/tex] ).

A sequence is an enumerated group of items in mathematics where repetitions are permitted and order is important. Similar to a set, it has members (also called elements, or terms). The length of the series is the number of elements (potentially infinite).

Given:

Ernie scores 50 points in Level 1 of a video game.

After II level the points would be

50 x 2 = 100

Then, after III level the points would be

100 x 2 = 200

So, the Recursive formula for the situation is

[tex]a_n[/tex]= a [tex]r^{n-1[/tex] where r is common ratio = 100/50 = 2

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Answer:

The formula for the surface area of a sphere with radius r is 4πr^2. Plugging in the given radius of 8, we get:

Surface area = 4π * 8^2 = 4π * 64 = 256π

Using an approximate value of π = 3.14, the surface area of the sphere is approximately:

256 * 3.14 = 803.84

Rounding to the nearest hundredth, the surface area of the sphere is approximately 803.84 square units.

Answer:

803.84cm²

Area of a sphere = 4πr²

When we put the given values we get

Area of a sphere = 4x3.14x8²

Area of a sphere = 4x3.14X16

                             = 804.25cm²

Rounding to the nearest hundredth we get,

803.84cm²

Answer:

Step-by-step explanation:

Given trains A and B have weights that total 147 tons, with train A being heavier by 65 tons, you want the weight of each.

The relations given in the problem can be expressed as ...

  A + B = 147 . . . . . . the total weight

  A - B = 65 . . . . . . . the difference of weights (A is heavier)

The equations can be added to eliminate the B variable:

  (A +B) +(A -B) = (147) +(65)

  2A = 212 . . . . simplify

  A = 106 . . . . . divide by 2

The other weight can be found any number of ways. One way is to subtract the difference here:

  B = A -65 = 106 -65 = 41

Train A weighs 106 tons; train B weighs 41 tons.

__

Additional comment

You will see "sum and difference" problems in many forms. The solution is always the same: the greater value is half the sum of the given numbers; the lesser value is half their difference.

  A = (147 +65)/2 = 212/2 = 106

  B = (147 -65)/2 = 82/2 = 41

(A) the x-intercepts of y = f(2x) are (-1)/2, 3/2, and 6/2.

(B) the x-intercepts of y = 2f(x) are 1, 3, and 6.

(C) the x-intercepts of y = f(x + 2) are (-1 - 2), (3 - 2), and (6 - 2), which are -3, 1, and 4.

(a) To find the x-intercepts of y = f(2x), we need to find the values of x for which f(2x) = 0. Since x-intercepts of y = f(x) are -1, 3, and 6, the corresponding x-intercepts of y = f(2x) are (-1)/2, 3/2, and 6/2.

(b) To find the x-intercepts of y = 2f(x), we need to find the values of x for which 2f(x) = 0. Since x-intercepts of y = f(x) are -1, 3, and 6, the x-intercepts of y = 2f(x) are the same: -1, 3, and 6.

(c) To find the x-intercepts of y = f(x + 2), we need to find the values of x for which f(x + 2) = 0. Since x-intercepts of y = f(x) are -1, 3, and 6, the corresponding x-intercepts of y = f(x + 2) are (-1 - 2), (3 - 2), and (6 - 2), which are -3, 1, and 4.

(d) The appearance of y = f(mx) will be a compression or expansion of the graph of y = f(x), depending on the value of m. If m < 1, the graph of y = f(mx) will be a compression of the graph of y = f(x) along the x-axis. If m > 1, the graph of y = f(mx) will be an expansion of the graph of y = f(x) along the x-axis. The x-intercepts of y = f(mx) can be found by finding the values of x for which f(mx) = 0.

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On solving the provided question we can say that Area of the base = [tex]pi*r^2 = 70[/tex] => 350 (3/70) = h = 15 m

The size of an area on a surface can be expressed as an area. The area of an open surface or the boundary of a three-dimensional object is referred to as the surface area, whereas the area of a planar region or planar region refers to the area of a form or planar layer. The total amount of space filled by a planar (2-D) surface or shape of an object is known as its area. Draw a square on a piece of paper using a pencil. a character with two dimensions. The area of a shape on paper is the space it takes up. Imagine that the square is composed of more compact unit squares.

[tex]pi * r^2 * h / 3[/tex]

Area of the base = [tex]pi*r^2 = 70[/tex]  

350 = 70 * h / 3  

350 = (70/3) * h    

350 (3/70) = h = 15 m

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Answer:

f(x) =[tex]\frac{10}{11}[/tex]x [tex]-\frac{16}{11}[/tex]

Step-by-step explanation:

The format of the linear function f(x) is ax + b. Thus, we can list the following equations:

4 = 6a + b .... (1)

-6 = -5a + b .... (2)

We can use the first equation to subtract the second equation getting: 10 = 11a. This means a = [tex]\frac{10}{11}[/tex]. From that, if we plug in the value of a into the first equation, we get 4 = [tex]\frac{60}{11}[/tex] + b, so b = [tex]-\frac{16}{11}[/tex]. Thus, f(x) =[tex]\frac{10}{11}[/tex]x [tex]-\frac{16}{11}[/tex]

The time that is taken by the colony is 23 years.

The exponential growth function can be used to account for the exponential increase in the number of the organisms that are to be found in the colony.

Given that we have that;

P=Poe^rt

P = Number at time t

Po = Number initially present

r = rate of growth

t = time taken

Thus;

3480 = 1120e^0.0498t

3480/1120 = e^0.0498t

3.1 = e^0.0498t

ln(3.1) = 0.0498t

t = ln3.1/0.0498

t = 23 years

There are 23 years

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Answer:

B) False

Step-by-step explanation:

It can be simplified to 3/7 as they both have the common factor 3.