UNIT CHECKPOINT:
Probability Distributions
Calculator
Suppose a normal distribution has a mean of 18 and a standard deviation of 4.
A value of 24 is how many standard deviations away from the mean?
-3
-1.5
1.5

9514 1404 393

Answer:

  50.24 cm

Step-by-step explanation:

Fill in the given numbers and do the arithmetic.

  s = rθ

  s = (24 cm)(2/3π) = (24 cm)(2/3)(3.14) = 50.24 cm

Step-by-step explanation:

the down function clearly is

y = x - 5, -2 <= x <= 8

the reasons :

1. it is linear. so, we have only a form of ax+b

2. x=0 => y=-5

x=5 => y=0

so, with these 2 points alone we can see

y = ax + b

-5 = a×0 +b = b

0 = a×5 - 5

5 = a×5

1 = a

the inverse function is based on

y = x - 5

=>

x = y + 5

now renaming the variables so that y is the result and x the input variable delivers

y = x + 5

and because the original function only delivered y- values between -7 and +3, this is also the defined domain for the inverse function.

so,

y = x + 5, -7 <= x <= +3

so, we have the points

x=-7 => y=-2

x=+3 => y=8

you need to draw the line between these 2 points with filled dots at the end points (as they are included in the function).

6

+

4

−

8

Step-by-step explanation:

Please mark me as brain list and please like my answer and rate also

Answer:

hope this will help you more

Answer:

[tex]{19}C_1=19[/tex]

Step-by-step explanation:

We need to find the value of [tex]{19}C_1[/tex].

C stands for combination.

The formula of combination is as follows :

[tex]nC_r=\dfrac{n!}{r!(n-r)!}[/tex]

Here,

n = 19 and r = 1

So,

[tex]nC_r=\dfrac{19!}{1!(19-1)!}\\\\nC_r=\dfrac{19!}{1!\times 18!}\\\\nC_r=\dfrac{19\times 18!}{1!\times 18!}\\\\nC_r=19[/tex]

So, the value of [tex]{19}C_1[/tex] is 19.

Answer:

Your answer will be 19C1 =19

Answer:

11/12

Step-by-step explanation:

1/4 + 2/3

= 3/12 + 8/12

= 11/12

Answer:

The probability that exactly 12 buyers would prefer green

=0.00555

Step-by-step explanation:

We are given that

p=50%=50/100=0.50

n=14

We have to find the probability that exactly 12 buyers would prefer green.

q=1-p

q=1-0.50=0.50

Using binomial distribution formula

[tex]P(X=x)=nC_r p^r q^{n-r}[/tex]

[tex]P(x=12)=14C_{12}(0.50)^{12}(0.50)^{14-12}[/tex]

[tex]P(x=12)=14C_{12}(0.50)^{12}(0.50)^2[/tex]

[tex]P(x=12)=14C_{12}(0.50)^{14}[/tex]

[tex]P(x=12)=\frac{14!}{12!2!}(0.50)^{14}[/tex]

[tex]P(x=12)=\frac{14\times 13\times 12!}{12!2\times 1}(0.50)^{14}[/tex]

[tex]P(x=12)=91\cdot (0.50)^{14}[/tex]

[tex]P(x=12)=0.00555[/tex]

Hence, the probability that exactly 12 buyers would prefer green

=0.00555

Find the values of the sine, cosine, and tangent for ∠A

a. sin A = [tex]\frac{\sqrt{13} }{2}[/tex],  cos A = [tex]\frac{\sqrt{13} }{3}[/tex],  tan A = [tex]\frac{2 }{3}[/tex]

b. sin A = [tex]3\frac{\sqrt{13} }{13}[/tex],  cos A = [tex]2\frac{\sqrt{13} }{13}[/tex],  tan A = [tex]\frac{3}{2}[/tex]

c. sin A = [tex]\frac{\sqrt{13} }{3}[/tex],  cos A = [tex]\frac{\sqrt{13} }{2}[/tex],  tan A = [tex]\frac{3}{2}[/tex]

d. sin A = [tex]2\frac{\sqrt{13} }{13}[/tex],  cos A = [tex]3\frac{\sqrt{13} }{13}[/tex],  tan A = [tex]\frac{2 }{3}[/tex]

d. sin A = [tex]2\frac{\sqrt{13} }{13}[/tex],  cos A = [tex]3\frac{\sqrt{13} }{13}[/tex],  tan A = [tex]\frac{2 }{3}[/tex]

The triangle for the question has been attached to this response.

As shown in the triangle;

AC = 36ft

BC = 24ft

ACB = 90°

To calculate the values of the sine, cosine, and tangent of ∠A;

i. First calculate the value of the missing side AB.

Using Pythagoras' theorem;

⇒ (AB)² = (AC)² + (BC)²

Substitute the values of AC and BC

⇒ (AB)² = (36)² + (24)²

Solve for AB

⇒ (AB)² = 1296 + 576

⇒ (AB)² = 1872

⇒ AB = [tex]\sqrt{1872}[/tex]

⇒ AB = [tex]12\sqrt{13}[/tex] ft

From the values of the sides, it can be noted that the side AB is the hypotenuse of the triangle since that is the longest side with a value of [tex]12\sqrt{13}[/tex] ft (43.27ft).

ii. Calculate the sine of ∠A (i.e sin A)

The sine of an angle (Ф) in a triangle is given by the ratio of the opposite side to that angle to the hypotenuse side of the triangle. i.e

sin Ф = [tex]\frac{opposite}{hypotenuse}[/tex]             -------------(i)

In this case,

Ф = A

opposite = 24ft (This is the opposite side to angle A)

hypotenuse = [tex]12\sqrt{13}[/tex] ft (This is the longest side of the triangle)

Substitute these values into equation (i) as follows;

sin A = [tex]\frac{24}{12\sqrt{13} }[/tex]

sin A = [tex]\frac{2}{\sqrt{13}}[/tex]

Rationalize the result by multiplying both the numerator and denominator by [tex]\sqrt{13}[/tex]

sin A = [tex]\frac{2}{\sqrt{13}} * \frac{\sqrt{13} }{\sqrt{13} }[/tex]

sin A = [tex]\frac{2\sqrt{13} }{13}[/tex]

iii. Calculate the cosine of ∠A (i.e cos A)

The cosine of an angle (Ф) in a triangle is given by the ratio of the adjacent side to that angle to the hypotenuse side of the triangle. i.e

cos Ф = [tex]\frac{adjacent}{hypotenuse}[/tex]             -------------(ii)

In this case,

Ф = A

adjacent = 36ft (This is the adjecent side to angle A)

hypotenuse = [tex]12\sqrt{13}[/tex] ft (This is the longest side of the triangle)

Substitute these values into equation (ii) as follows;

cos A = [tex]\frac{36}{12\sqrt{13} }[/tex]

cos A = [tex]\frac{3}{\sqrt{13}}[/tex]

Rationalize the result by multiplying both the numerator and denominator by [tex]\sqrt{13}[/tex]

cos A = [tex]\frac{3}{\sqrt{13}} * \frac{\sqrt{13} }{\sqrt{13} }[/tex]

cos A = [tex]\frac{3\sqrt{13} }{13}[/tex]

iii. Calculate the tangent of ∠A (i.e tan A)

The cosine of an angle (Ф) in a triangle is given by the ratio of the opposite side to that angle to the adjacent side of the triangle. i.e

tan Ф = [tex]\frac{opposite}{adjacent}[/tex]             -------------(iii)

In this case,

Ф = A

opposite = 24 ft (This is the opposite side to angle A)

adjacent = 36 ft (This is the adjacent side to angle A)

Substitute these values into equation (iii) as follows;

tan A = [tex]\frac{24}{36}[/tex]

tan A = [tex]\frac{2}{3}[/tex]

Answer:

I think C

Step-by-step explanation:

Sorry if its wrong

Answer:

865 in the workforce should be interviewed to meet your requirements

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].

The margin of error is given by:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

A pilot survey reveals that 5 of the 50 sampled hold two or more jobs.

This means that [tex]\pi = \frac{5}{50} = 0.1[/tex]

95% confidence level

So [tex]\alpha = 0.05[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].

How many in the workforce should be interviewed to meet your requirements?

Margin of error of 2%, so n for which M = 0.02.

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.02 = 1.96\sqrt{\frac{0.1*0.9}{n}}[/tex]

[tex]0.02\sqrt{n} = 1.96\sqrt{0.1*0.9}[/tex]

[tex]\sqrt{n} = \frac{1.96\sqrt{0.1*0.9}}{0.02}[/tex]

[tex](\sqrt{n})^2 = (\frac{1.96\sqrt{0.1*0.9}}{0.02})^2[/tex]

[tex]n = 864.4[/tex]

Rounding up:

865 in the workforce should be interviewed to meet your requirements

Answer:

Step-by-step explanation:

Frt7v6c87buhinjomp,l.;

Answer:

I'm pretty sure it's 8x^2+20xy-12y^2

Answer:

pff don't know .  sssory

Step-by-step explanation:

Cross sections of the volume are washers or annuli with outer radii x(y) + 1, where

y = x(y) ² - 1   ==>   x(y) = √(y + 1)

and inner radii 1. The distance between the outermost edge of each shell to the axis of revolution is then 1 + √(y + 1), and the distance between the innermost edge of R on the y-axis to the axis of revolution is 1.

For each value of y in the interval [-1, 3], the corresponding cross section has an area of

π (1 + √(y + 1))² - π (1)² = π (2√(y + 1) + y + 1)

Then the volume of the solid is the integral of this area over [-1, 3]:

[tex]\displaystyle\int_{-1}^3\pi y\,\mathrm dy = \frac{\pi y^2}2\bigg|_{-1}^3 = \boxed{4\pi}[/tex]

[tex]\displaystyle\int_{-1}^3 \pi\left(2\sqrt{y+1}+y+1\right)\,\mathrm dy = \pi\left(\frac43(y+1)^{3/2}+\frac{y^2}2+y\right)\bigg|_{-1}^3 = \boxed{\frac{56\pi}3}[/tex]

Answer:

0.64 = 64% probability that the student passes both subjects.

0.86 = 86% probability that the student passes at least one of the two subjects

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

P(B|A) is the probability of event B happening, given that A happened.

[tex]P(A \cap B)[/tex] is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Passing subject A

Event B: Passing subject B

The probability of passing subject A is 0.8.

This means that [tex]P(A) = 0.8[/tex]

If you have passed subject A, the probability of passing subject B is 0.8.

This means that [tex]P(B|A) = 0.8[/tex]

Find the probability that the student passes both subjects?

This is [tex]P(A \cap B)[/tex]. So

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

[tex]P(A \cap B) = P(B|A)P(A) = 0.8*0.8 = 0.64[/tex]

0.64 = 64% probability that the student passes both subjects.

Find the probability that the student passes at least one of the two subjects

This is:

[tex]p = P(A) + P(B) - P(A \cap B)[/tex]

Considering [tex]P(B) = 0.7[/tex], we have that:

[tex]p = P(A) + P(B) - P(A \cap B) = 0.8 + 0.7 - 0.64 = 0.86[/tex]

0.86 = 86% probability that the student passes at least one of the two subjects

Answer:

7-i

Step-by-step explanation:

It is asking for the product of the given complex numbers.

Z1Z2 means Z1 times Z2

(1+i)(3-4i)

You can do the whole foil thing here since we are multiplying a pair of binomials. But all you are doing when you do that is multiplying every term in the first ( ) to every term in the second ( ).

1(3)+1(-4i)+i(3)+i(-4i)

Simplify each term. That is, perform the multiplication in each term:

3-4i+3i-4i^2

Combine like terms and also replace i^2 with (-1):

3-1i-4(-1)

Multiplication identity property used:

3-i+4

Combine like terms:

7-i

Answer: 1/50, or 0.02

Step-by-step explanation:

I'm assuming this is 5*10/25/100. if you just follow the equation, you get 50/25/100, which is 2/100, or 1/50.

Answer:

265

Step-by-step explanation:

9514 1404 393

Answer:

  265

Step-by-step explanation:

Let t represent the number of tiles needed. Then the area covered by those t tiles will be ...

  area = t·0.34 ft²

We want that area to be 90 ft², so we can solve this equation for t:

  90 ft² = t·(0.34 ft²)

  90 ft²/(0.34 ft²) = t ≈ 264.71

About 265 tiles are needed to cover 90 ft².

Answer: The rise and run is the two point between each other on a line for example 1/2 rise over run. 1 is rise and 2 is run so y=mx +b the slope is m and the y int is b so

Y= 1/2x + 3 the 3 is going to be on the Y acis not the X its important not to mix the two. In other words go to 0,0 make a line go up.. the from 0,0 go doen the same length

Step-by-step explanation:

Answer:

17%

Step-by-step explanation:

change in temprature=100-120=-20

% chsnge in temp.=-20/120 ×100=-50/3 %=-16.66666...≈-17%

negative sign shows temperature is coming down.

Answer:

1.

a. 2

b. 0.1353 probability that exactly 0 customers will arrive during a five-minute period, 0.2707 that exactly 1 customer will arrive, 0.2707 that exactly 2 customers will arrive and 0.1805 that exactly 3 customers will arrive.

c. 0.1428 = 14.28% probability that delays will occur.

2.

a. 0.4512 = 45.12% probability that the service time is one minute or less.

b. 0.6988 = 69.88% probability that the service time is two minutes or less.

c. 0.3012 = 30.12% probability that the service time is more than two minutes.

Step-by-step explanation:

Poisson distribution:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

In which

x is the number of sucesses

e = 2.71828 is the Euler number

[tex]\mu[/tex] is the mean in the given interval.

Exponential distribution:

The exponential probability distribution, with mean m, is described by the following equation:

[tex]f(x) = \mu e^{-\mu x}[/tex]

In which [tex]\mu = \frac{1}{m}[/tex] is the decay parameter.

The probability that x is lower or equal to a is given by:

[tex]P(X \leq x) = \int\limits^a_0 {f(x)} \, dx[/tex]

Which has the following solution:

[tex]P(X \leq x) = 1 - e^{-\mu x}[/tex]

The probability of finding a value higher than x is:

[tex]P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}[/tex]

Question 1:

a. What is the mean or expected number of customers that will arrive in a five-minute period?

0.4 customers per minute, so for 5 minutes:

[tex]\mu = 0.4*5 = 2[/tex]

So 2 is the answer.

Question b:

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

[tex]P(X = 0) = \frac{e^{-2}*2^{0}}{(0)!} = 0.1353[/tex]

[tex]P(X = 1) = \frac{e^{-2}*2^{1}}{(1)!} = 0.2707[/tex]

[tex]P(X = 2) = \frac{e^{-2}*2^{2}}{(2)!} = 0.2707[/tex]

[tex]P(X = 3) = \frac{e^{-2}*2^{3}}{(3)!} = 0.1805[/tex]

0.1353 probability that exactly 0 customers will arrive during a five-minute period, 0.2707 that exactly 1 customer will arrive, 0.2707 that exactly 2 customers will arrive and 0.1805 that exactly 3 customers will arrive.

Question c:

This is:

[tex]P(X > 3) = 1 - P(X \leq 3)[/tex]

In which:

[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)[/tex]

The values we have in item b, so:

[tex]P(X \leq 3) = 0.1353 + 0.2707 + 0.2707 + 0.1805 = 0.8572[/tex]

[tex]P(X > 3) = 1 - P(X \leq 3) = 1 - 0.8572 = 0.1428[/tex]

0.1428 = 14.28% probability that delays will occur.

Question 2:

[tex]\mu = 0.6[/tex]

a. What is the probability that the service time is one minute or less?

[tex]P(X \leq 1) = 1 - e^{-0.6} = 0.4512[/tex]

0.4512 = 45.12% probability that the service time is one minute or less.

b. What is the probability that the service time is two minutes or less?

[tex]P(X \leq 2) = 1 - e^{-0.6(2)} = 1 - e^{-1.2} = 0.6988[/tex]

0.6988 = 69.88% probability that the service time is two minutes or less.

c. What is the probability that the service time is more than two minutes?

[tex]P(X > 2) = e^{-1.2} = 0.3012[/tex]

0.3012 = 30.12% probability that the service time is more than two minutes.

Answer:

4,-1 that is the answer so

Answer:

It should be the top right one

(with 6ft as the height)

Step-by-step explanation:

Answer:

It must be the lower to the left choice.

Step-by-step explanation:

As you can see, the net we have is composed of only triangles.

So we should be choosing a figure with a triangular base.

Our answers are narrowed down into the top right and lower left choices because both figures have triangular bases.

The other person down there chose the top right choice and was incorrect, so the answer should be the lower to the left figure.

Also, its the lower left figure because look at the triangular base, it is an isosceles meaning that two sides have the same length.

If the net says that the long side measures 9 ft, then the other two sides should be the same length and shorter than 9 ft. So the answer is the lower left figure.

Hope this helps

Answer:

13/17

Step-by-step explanation:

9514 1404 393

Answer:

  -16∛2

Step-by-step explanation:

It can be helpful to have some familiarity with the cubes of small integers. For example, ...

  2³ = 8

  6³ = 216

With this in mind you recognize the expression as ...

  3∛((-6)³(2)) +∛((2³)(2))

  = 3(-6)∛2 +2∛2

  = (-18 +2)∛2

  = -16∛2

Answer:

7/4 is larger than -4/7

Step-by-step explanation:

7/4 is greater than a whole. 4/4 = 1 whole and the fraction is 7/4. -4/7 is smaller than a whole and is a negative number.

Therefore 7/4 is bigger

Hope this helps!

Answer:

yes 7/4 is bigger than -4/7

Step-by-step explanation:

its bigger because its positive!

Answer:

I'm going to help you figure this out because I am actually on the same assignment. If you do not understand what it is asking, it is not asking you to break down the function notation, it is simply asking you to substitute (X) with 2,3,4,5,and 6 and then to solve it on each line

Answer:

16x4−4x2+4x−116x4−4x2+4x−1

=16x4−(4x2−4x+1)=16x4−(4x2−4x+1)

=(4x2)2−(2x−1)2∵a2−2ab+b2=(a−b)2=(4x2)2−(2x−1)2∵a2−2ab+b2=(a−b)2

=(4x2−2x+1)(4x2+2x−1)∵a2−b2=(a−b)(a+b

Step-by-step explanation:

Answer:

yes your answer is right

Answer:

Yes it's Perfectly correct

Answer:

[tex]x = - \frac{1}{2} [/tex]

Step-by-step explanation:

[tex]x = \frac{ - b}{2a} = \frac{1}{ - 2} [/tex]