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Chapter 7: Q.15 (page 430)

Run a mile During World War II, able-bodied male undergraduates at the University of Illinois participated in required physical training. Each student ran a timed mile. Their times followed the Normal distribution with mean 7.11minutes and standard deviation 0.74minute. An SRS of 100of these students has mean time x炉=7.15minutes. A second SRS of size100has mean x炉=6.97minutes. After many SRSs, the values of the sample mean x follow the Normal distribution with mean 7.11 minutes and standard deviation0.074minute.

(a) What is the population? Describe the population distribution. (b) Describe the sampling distribution of x. How is it different from the population distribution?

Short Answer

Expert verified

a). The population distribution is a Normal distribution.

b). Average time to run a mile of 100students from the population. Smaller standard deviation.

Step by step solution

01

Part (a) Step 1: Given Information 

The values of the sample mean x follow the Normal distribution with mean 7.11 minutes and a standard deviation of 0.074 minute.

02

Part (a) Step 2: Explanation 

Individuals who are being examined make up the population.

POPULATION=12000able-bodied male undergraduates from the University of Illinois who took part in World War II physical training.

The population distribution is given as a Normal distribution with a mean of 7.11minutes and a standard deviation of 0.74minutes, corresponding to the time it takes for randomly selected individuals to run a mile.

03

Part (b) Step 1: Given Information 

The values of the sample mean x follow the Normal distribution with mean 7.11 minutes and standard deviation 0.074 minute

04

Part (b) Step 2: Explanation 

The sample mean x炉values are distributed normally, with a mean of 7.11minutes and a standard deviation of 0.074minutes.

As a result x炉's sample distribution is the Normal distribution, with a mean of 7.11minutes and a standard deviation of 0.074minutes.

The x炉sample distribution describes the average time taken by 100students from the population to run a mile.

The reduced standard deviation distinguishes it from the population distribution.

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