SOLUTION: 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 dista

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Question 1203005: 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 210.90 cm. b. find the probability that the mean 15 for 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 30?
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
mean is 197.5
sandard deviation is 8.9
proability of individual distance greater than 210.90 is equal to .0661.

if sample size is 15, then standard error = 8.9 / sqrt(15) = 2.29797
probability of getting the mean of the sample to be greaer than 196.2 is equal to .71422

the normal distribution can be used in part b, even though the sample size is less than 30, because the population is normally distributed.

here's what it looks like with an online calculator.