Question

Assume that​ women's heights are normally distributed with a mean given by

μ=63.6 in​,

and a standard deviation given by

σ=2.7 in.

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

​(b) If 47 women are randomly​ selected, find the probability that they have a mean height less than 64 in.

Answer 1

We are given the distribution of heights here as:

a) Probability here is computed as:
P(X < 64)

Converting it to a standard normal variable, we have here:

Getting it from the standard normal tables, we have here:

Therefore 0.5589 is the required probability here.

b) For sample size = 47, as it is greater than 30, we can apply the Central Limit theorem to get the required probability here as:

Converting it to a standard normal variable, we have here:

Getting it from the standard normal tables, we have here:

Therefore 0.8451 is the required probability here.