Using the Central Limit Theorem Use this information about t

Using the Central Limit Theorem. Use this information about the overhead reach distances of adult females:205.5 cm, 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. If 25 adult females are randomly selected, find the probability that they have a mean overhead reach greater than 203.0 cm

Solution

suppose that x is the overhead reach distnace of females

mean of overhead reach distance = 107.05

variance of overhead reach distance = 19384.81

now using centarl limit theorem mean overhead reach distance follows normal distribution with mean 107.05 and varaince =19384.81/25.

mnow standard deviation of data = sqrt(19384.81/25) = 139.2293 / 5

we are required to find

p(mean>203)

p((mean-107.05)*5/139.2293 > (203-107.05)*5/139.2293 )

=(z>3.445754)

0.0002847343