Heights of women (in inches) are approximately N(64.5,2.5) distributed. Compute the probability that the average height of 25 randomly selected women will be bigger than 66 inches.

Answers

Answer 1

Answer:

Answer:

the probability that the average height of 25 randomly selected women will be bigger than 66 inches is 0.0013

Step-by-step explanation:

From the summary of the given statistical dataset

The mean and standard deviation for the sampling distribution of sample mean of 25 randomly selected women can be calculated as follows:

$\mu_(\overline x) = \mu _x$ = 64.5

$\sigma_(\overline x )= (\sigma)/(\sqrt n)$

$\sigma_(\overline x )= \frac{2.5}{\sqrt {25}}$

$\sigma_(\overline x )= (2.5)/(5)$

$\sigma_(\overline x )$ = 0.5

Thus X $\sim$ N (64.5,0.5)

Therefore, the probability that the average height of 25 randomly selected women will be bigger than 66 inches is:

$P(\overline X > 66) = P ( (\overline X - \mu_\overline x)/(\sigma \overline x )>(66 - 64.5)/(0.5) })$

$P(\overline X > 66) = P ( Z>(66 - 64.5)/(0.5) })$

$P(\overline X > 66) = P ( Z>(1.5)/(0.5) })$

$P(\overline X > 66) = P ( Z>3 })$

$P(\overline X > 66) = 1- P ( Z<3 })$

$P(\overline X > 66) = 1- 0.9987$

$P(\overline X > 66) =0.0013$

the probability that the average height of 25 randomly selected women will be bigger than 66 inches is 0.0013

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(3x^2+2x-1)-(x^2-3x+4)

Answers

To evaluate the expression we shall have:
(3x^2+2x-1)-(x^2-3x+4)
putting like terms together we get:
(3x^2-x^2)+(2x+3x)+(-1-4)
=2x^2+5x-5
Answer: 2x^2+5x-5

What is the equation of the line that passes through the point (-8,5) and has a slope
of o?

Answers

Answer: y = 5

Step-by-step explanation:

If the slope is 0, the graph of the line is a horizontal line (parallel to the x-axis). 0 slope means it is flat.

Here it passes through the y-axis at +5 and passes through every value of x.

Final answer:

The equation of a line with slope 0 that passes through the point (-8,5) is y = 5.

Explanation:

The equation of a line can be found using the slope-intercept form y = mx + b, where 'm' represents the slope and 'b' is the y-intercept. The given slope of the line is 0, which means the line is horizontal with equation y = b. However, our line needs to pass through the point (-8,5), and at this point, the y coordinate is 5. Hence, for this line, b equals 5. So, the equation of the line is y = 5.

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Find the area of shaded region

Answers

Answer:

180

Step-by-step explanation:

calculate the non shaded parts first:

[FBE]=60

[DAE]=40

[ABCD]=280

so if we were to subtract the non shaded parts from the total area, we would get the shaded region. therefore, the shaded region is 180

The equation T^2=A^3 shows the relationship between a planet’s orbital period, T, and the planet’s mean distance from the sun, A, in astronomical units, AU. If planet Y is twice the mean distance from the sun as planet X, by what factor is the orbital period increased?

Answers

the answer for your question is going to be. 2^((3)/(2)) I know this cause I just took a quiz with this question on it

Answer:

2 Superscript three-halves

Step-by-step explanation:

Edge

given f(7)=4, f'(7)=10, g(7)=-1, g'(7)=8, find the values of the following: 1. (fg)'(7) = 2. (f/g)'(7) =

Answers

By the product rule,

$(fg)'=f'g+fg'$

so that

$(fg)'(7)=f'(7)g(7)+f(7)g'(7)=10\cdot(-1)+4\cdot8=22$

By the quotient rule,

$\left(\frac fg\right)'=(f'g-fg')/(g^2)$

so that

$\left(\frac fg\right)'(7)=(f'(7)g(7)-f(7)g'(7))/(g(7)^2)=(10\cdot(-1)-4\cdot8)/((-1)^2)=-42$

(g) If each customer takes 3 minutes to check out, what is the probability that it will take more than 6 minutes for all the customers currently in line to check out? The probability that it will take more than 6 minutes for all the customers currently in line to

Answers

The probability that it will take more than 6 minutes for all the customers in line to check out is 0.40.

We are given the probability distribution of x, the number of customers in line at a supermarket express checkout counter.

Moreover, we are given that each customer takes 3 minutes to check out.

It means that if there are 0 customers in line, i.e., x=0, then it will take 0 minutes for all the customers currently in line to check out.

If there is 1 customer in line, i.e., x=1, then it will take 3 minutes for all the customers currently in line to check out.

If there are 2 customers in line, i.e., x=2, then it will take 6 minutes for all the customers currently in line to check out.

If there are 3 customers in line, i.e., x=3, then it will take 9 minutes for all the customers currently in line to check out.

If there are 4 customers in line, i.e., x=4, then it will take 12 minutes for all the customers currently in line to check out.

If there are 5 customers in line, i.e., x=5, then it will take 15 minutes for all the customers currently in line to check out.

From above we note that if there are 3 or more customers in the line, then it will take more than 6 minutes (note that the case of check out time equal to 6 minutes is not included when we want 'more than 6 minutes') for all the customers currently in line to check out.

Thus, required probability is given by:

P(more than 6 minutes for all the customers currently in line to check out) = P(x ≥ 3)

= P(x=3) + P(x=4) + P(x=5)

= 0.20 + 0.15 + 0.05

= 0.40

Therefore, the probability that it will take more than 6 minutes for all the customers in line to check out is 0.40.

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Final answer:

Without specific information on the total number of customers or the distribution of customers in line, we cannot calculate a specific probability for it to take more than 6 minutes for all customers to check out, given that each customer takes 3 minutes.

Explanation:

The question is about the probability that it will take more than 6 minutes for all the customers in line to check out, given that each customer takes 3 minutes. The time it takes for all the customers to check out is determined by the number of customers in line. If there are two or more customers in line, it will definitely take more than 6 minutes for all of them to check out, because the checkout time is 3 minutes per customer.

So, the question of probability relates to the likelihood of there being two or more customers in line. Without information on the total number of customers, or the distribution of customers in line, we cannot calculate a specific probability.

Please note, this is a practical application of topics in probability and queue theory, involving concepts like mean arrival rate and service rate.

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