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Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
ISBN: 9781133956570

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Section
BuyFindarrow_forward

Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
ISBN: 9781133956570
Textbook Problem

A survey of high school seniors shows that the average wake-up time the previous Saturday morning was μ = 9:45. Assume that the distribution of times is approximately normal with a standard deviation of σ = 65 minutes, and find each of the requested values.

a. What proportion of high school seniors wake up later than 11:00?

b. What is the probability of randomly selecting a high school senior who woke up before 9:00?

c. What is the probability of obtaining a mean wake-up time earlier than M = 9:30 for a sample of n = 25 high school students?

(a)

To determine

To find: The proportion of high school senior’s wakeup later than 11:00.

Explanation

Given info:

The random variable X denote the distribution of times follows the normal distribution with mean of μ=9:45 and standard deviation of σ=65minutes.

Calculation:

The formula for z score is,

z=Xμσ

Substitute the value 9:45(585 minutes) for μ, 11:00(660 minutes) for X and 65 minutes for σ.

z=66058565=1

(b)

To determine

To find: The probability of randomly selecting a high school senior who woke up before 9:00.

(c)

To determine

To find: The probability of obtaining a mean woke up earlier 9:30.

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