The mean height of men is 69 inches with a standard deviatio

The mean height of men is 69 inches with a standard deviation of 3 inches. You may assume that men\'s heights are normally distributed.

a. What is the probabilty of a randomly selected man being shorter than 63 inches?

b. Among groups of 23 men, what do we expect the average height to be? What is the standard deviation?

c. Suppose the mean height of 23 random men in my stats classes is 70 inches. What percentile is this relative to other groups of size 23?

d. What is the probability of a group of 23 men having a mean height less than 63 inches?

Solution

a)

z =(63-69)/3 = -2

Probability = 0.0228 Answer

b)

Average height will be still : 69 inches

Standard deviation = 3/sqrt(23) = 0.63 Answer

c)

Percentile = 69/70 * 100 = 98.57% Answer

d)

z =(63-69)/3/(sqrt(23)) = -0.42

Probability = 0.3372 Answer