Question

Assume that women’s heights are normally distributed with a mean given by μ=63.5

in, and a standard deviation given by σ=3.1 in.
a. If 1 woman is randomly selected, find the probability that her height is less than 64 in.
The probability is approximately _______________________.
b. If 44 women are randomly selected, find the probability that they have a mean height
less than 64 in.
The probability is approximately _______________________.

Answer 1

Answer:64.3738

Explanation:

Answer 2

Part a) 0.5636 or 56.36%

Explanation:

Part a)

Given the info on mean and standard deviation, we evaluate the Z-score as:

Z = (64 - 63.5)/3.1 = 0.16

and use the Z-tables to find that

P(x < 64) = 0.5636 = 56.36%