Question

Assume that the heights of women are normally distributed with a mean of 63.6 inches and a standard deviation of 2.5 inches. a) Find the probability that if an individual woman is randomly selected, her height will be greater than 64 inches. b) Find the probability that 16 randomly selected women will have a mean height greater than 64 inches.

Answer 1

solution:

mean = inch.

standard deviation = inch

a) we have to find the prbabiity of randoml selected women's height more than 64 inches = P(X > 64)

now calculating the z score

P(X > 64) 1 - value of z to the left of 0.16 = 1 - 0.5636 = 0.4364

b)

if we selected 16 women randomly , probability that their mean height is greater than 64 = P(M > 64)

finding z score

P(M > 64) = 1 - value of z to the left of 0.64 = 1 - 0.7389 = 0.2611