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Introductory Statistics

Barbara Illowsky, Susan Dean

$Math Studyset Vaia Explanations$ Math

OER 2018 Edition · 902 pages

ISBN: 9781938168208

Chapter 7: Q.12 (page 428)

Find the probability that the sum of the $40$ values is less than $7, 000$ .

Short Answer

Expert verified

The probability that the sum of the $40$ values is less than $7000$ is $P (X \leq 7000) = 0.0569$ .

Step by step solution

01

Given Information

A mean ( $μ_{x}$ ) is $180$ and a standard deviation $(σ)$ is $20$ .

02

Explanation

To find the probability that the sums of the $40$ values is less than $7000$ :

localid="1649346312817" $\sum X ~ N (n μ_{x}, \sqrt{n} σ_{x})$

$\sum X ~ N ((40) (180), (\sqrt{40}) (20))$

localid="1649346327071" $P (X \leq 7000) = P (Z \leq \frac{X - n μ_{x}}{\sqrt{n} σ_{x}}) = P (Z \leq \frac{7000 - 7200}{126.4911}) = P (Z \leq - 1.5811)$

P (X \leq 7000) = 0.0569

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Most popular questions from this chapter

Yoonie is a personnel manager in a large corporation. Each month she must review $16$ of the employees. From past experience, she has found that the reviews take her approximately four hours each to do with a population standard deviation of $1.2$ hours. Let Χ be the random variable representing the time it takes her to complete one review. Assume Χ is normally distributed. Let $\bar{x}$ be the random variable representing the meantime to complete the $16$ reviews. Assume that the $16$ reviews represent a random set of reviews.

Find the $95$ th percentile for the meantime to complete one month's reviews. Sketch the graph.

a.

b. The $95$ th Percentile =____________

The average wait time is:

a. one hour.

b. two hours.

c. two and a half hours.

d. four hours.

An unknown distribution has a mean of $80$ and a standard deviation of $12$ . A sample size of $95$ is drawn randomly from the population.

Find the probability that the sum of the $95$ values is greater than $7650$ .

What's the approximate probability that the average price for $16$ gas stations is over localid="1648486706621" $$ 4.69$ ?

a. almost zero

b. $0.1587$

c. $0.0943$

d. unknown

Find the sum with a $z$ –score of $0.5$ .

See all solutions

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