statistics question

Question

Men have a mean height of 68.6 inches with a standard deviation of 2.8 inches. What proportion of men are taller than 72 inches?

Answer 1

Ok so the data has a normal distribution with a mean of 68.6 inches and standard deviation of 2.8 inches. The proportion of people who are taller than a specific height is equal to the probability of someone being taller than a specific height. So lets treat people's heights as variable X. What you are asking is P(X>72), since X follows the normal distribution we can convert X to Z, where Z follows a standard normal distribution with a mean of 0 and a standard deviation of 1 Z = (X - mean) / standard deviation

P(X>72) = P(Z>(72-68.6)/2.8) = P(Z>1.21), now you would want to use a normal distribution table to look up the value of 1.21. Most tables provide you with P(Z<1.21) which equals 0.8869, To get P(Z>1.21) = 1-P(Z<1.21) = 1-.8869 = .1131, so the proportion of people who would be over 72 inches is 11.31% of people.

So your answer would be 11.31% of people would be taller than 72 inches.