Question

Assume that women's heights are normally distributed with a mean given by u=63.6in and a standard deviation given by = 2.7in.

a) if 1 woman is randomly selected, find the probability that her height is less than 64in.

b) If 50 women are randomly selected, find the probability that they have a mean height less than 64in.

Answer 1

Part a):First we need to find the z-score.

z-score formula:

                         =

In excel :

P(x<64) = 0.558887

Part b): Now we find the probability that they have a mean height less than 64in but the 50 women is selected.

sample size =50 (which is the large sample size )

So we can use the central limit theorem.

Central limit stated that the sample size is large that is greater than 30 then use central limit theorem with mean mu and standard deviation sigma/square root of n.