Question

The overhead reach distance of adult females is normally distributed with a mean of 205 cm and a standard deviation of 7.8 cm.

1) Find the probability that an individual distance is greater than 214.30 cm.

2) Find the probability that the mean for 20 randomly selected distances is greater than 203.20 cm.

3) Why can the normal distribution be used in part B, even though the sample size does not exceed 30?

Answer 1

let X is overhead reach distance of adults females so

X is normal with mean=205 SD=7.8

a)

we have to find P(X>214.30)

now

b)

for n=20 we have to find sample mean >203.20

now

c)

normal distribution be used in part B, even though the sample size does not exceed 30 because we have taken samples from Normal population as The overhead reach distance of adult females is normally distributed with a mean of 205 cm and a standard deviation of 7.8 cm.