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The overhead reach distances of adult females are normally distributed with a mean of 205 om and a standard deviation of 8.6 cm. a. Find the probability that an individual distance is greater than 214.30 cm. b. Find the probability that the mean for 20 randomly selected distances is greater than 203.20 cm. c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30?

The overhead reach distances of adult females are normally distributed with a mean of 205 om and a standard deviation of 8.6 cm. a. Find the probability that an individual distance is greater than 214.30 cm. b. Find the probability that the mean for 20 randomly selected distances is greater than 203.20 cm. c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30?

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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The overhead reach distances of adult females are normally distributed with a mean of 205 cm and a standard deviation of 8.6 cm. a. Find the probability that an individual distance is greater than 214.30 cm. b. Find the probability that the mean for 20 randomly selected distances is greater than 203.20 cm. c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30? 2. The probability is D. (Round to four decimal places as needed.)
Transcribed Image Text:The overhead reach distances of adult females are normally distributed with a mean of 205 cm and a standard deviation of 8.6 cm. a. Find the probability that an individual distance is greater than 214.30 cm. b. Find the probability that the mean for 20 randomly selected distances is greater than 203.20 cm. c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30? 2. The probability is D. (Round to four decimal places as needed.)
An engineer is going to redesign an ejection seat for an airplane. The seat was designed for pilots weighing between 130 lb and 181 Ib. The new population of pilots has normally distributed weights with a mean of 138 ib and a standard deviation of 32.6 lb. Click here to view page 1 of the standard normal distribution. Click here to view page 2 of the standard normal distribution. a. If a pilot is randomly selected, find the probability that his weight is between 130 lb and 181 Ib. The probability is approximately- (Round to four decimal places as needed.)
Transcribed Image Text:An engineer is going to redesign an ejection seat for an airplane. The seat was designed for pilots weighing between 130 lb and 181 Ib. The new population of pilots has normally distributed weights with a mean of 138 ib and a standard deviation of 32.6 lb. Click here to view page 1 of the standard normal distribution. Click here to view page 2 of the standard normal distribution. a. If a pilot is randomly selected, find the probability that his weight is between 130 lb and 181 Ib. The probability is approximately- (Round to four decimal places as needed.)
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