The overhead reach distances of adult females are normally distributed with a mean of 200 cm and a standard deviation of 7.8 cm. a. Find the probability that an individual distance is greater than 209.30 cm. b. Find the probability that the mean for 20 randomly selected distances is greater than 197.80 cm. c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30?

A First Course in Probability (10th Edition)
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Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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I need the solutions for A,B and C please?

The overhead reach distances of adult females are normally distributed with a mean of 200 cm and a standard deviation
of 7.8 cm.
a. Find the probability that an individual distance is greater than 209.30 cm.
b. Find the probability that the mean for 20 randomly selected distances is greater than 197.80 cm.
c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30?
Transcribed Image Text:The overhead reach distances of adult females are normally distributed with a mean of 200 cm and a standard deviation of 7.8 cm. a. Find the probability that an individual distance is greater than 209.30 cm. b. Find the probability that the mean for 20 randomly selected distances is greater than 197.80 cm. c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30?
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