The overhead reach distances of adult females are normally distributed with a mean of 197.5 cm and a standard deviation of 8.9 cm a. Find the probability that an individual distance is greater than 210.00 cm. b. Find the probability that the mean for 15 randomly selected distances is greater than 196.20 cm. c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30? a. The probability is (Round to four decimal places as needed.)

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
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The overhead reach distances of adult females are normally distributed with a mean of 197.5 cm and a standard deviation of 8.9 cm
a. Find the probability that an individual distance is greater than 210.00 cm.
b. Find the probability that the mean for 15 randomly selected distances is greater than 196.20 cm.
c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30?
a. The probability is
(Round to four decimal places as needed.)
Transcribed Image Text:The overhead reach distances of adult females are normally distributed with a mean of 197.5 cm and a standard deviation of 8.9 cm a. Find the probability that an individual distance is greater than 210.00 cm. b. Find the probability that the mean for 15 randomly selected distances is greater than 196.20 cm. c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30? a. The probability is (Round to four decimal places as needed.)
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