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Get Full Access to Elementary Statistics - 12 Edition - Chapter 6.5 - Problem 8bsc
Get Full Access to Elementary Statistics - 12 Edition - Chapter 6.5 - Problem 8bsc

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# Using the Central Limit Theorem. In Exercises use this

ISBN: 9780321836960 18

## Solution for problem 8BSC Chapter 6.5

Elementary Statistics | 12th Edition

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Problem 8BSC

Problem 8BSC

Using the Central Limit Theorem. In Exercises use this information about the overhead reach distances of adult females:μ = 205.5 cm,σ = 8.6 cm, and overhead reach distances are normally distributed (based on data from the Federal Aviation Administration). The overhead reach distances are used in planning assembly work stations.

a. If 1 adult female is randomly selected, find the probability that her overhead reach is greater than 195.0 cm.

b. If 25 adult females are randomly selected, find the probability that they have a mean overhead reach greater than 203.0 cm.

c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30?

Step-by-Step Solution:
Step 1 of 3

Solution 8BSC

1. If 1 adult female is randomly selected, the probability that her overhead reach is greater than 195.0 cm is 0.8889.
2. If 25 adult female is randomly selected, the probability that her overhead reach is greater than 203.0 cm is 0.9270.
3. The normal distribution can be used in part (b), even though the sample size does not exceed 30 because the original population is normal and the distribution of the sample means is normal for any sample size.

Step 2 of 3

Step 3 of 3