Statistics question

Question

Adult male height is normally distributed with a mean of 69 inches and a standard deviation of 2.29 inches. If an adult male is randomly selected, what is the probability that the adult male has a height between 64.6 and 69.1 inches? Round your final answer to four decimal places.

Answer 1

On this type of question you want to first use the formula

z = (x – mean) / (standard deviation) in order to convert the given values over into a Z score. then once you have done that you can use technology like a calculator or Microsoft Excel to convert the value over into a probability.

From the values in the question we get

z = (64.6 – 69)/2.29 = -1.9214

z = (69.1 – 69)/2.29 = 0.0437

for the Z values

using technology to convert that over then I get 0.4900 for the resulting probability