Question

11. Suppose the heights of a population of people are normally distributed with a mean of 70.5 inches and a standard deviation of 2.7 inches.

a. Find the probability that a randomly selected person from this population is between 67.2 and 71.2 inches tall. (7 points)

b. What height denotes the 95th percentile? (5 points)

Answer 1

Solution :

Given that ,

mean = = 70.5

standard deviation = = 2.7

a)

P(67.2 < x < 71.2) = P((67.2 - 70.5)/ 2.7) < (x - ) /  < (71.2 - 70.5) / 2.7) )

= P(-1.22 < z < 0.26)

= P(z < 0.26) - P(z < -1.22)

= 0.6026 - 0.1112

= 0.4914

Probability = 0.4914

b)

P(Z < z ) = 95%

P(Z < z ) = 0.95

P(Z < 1.645) = 0.95

z = 1.645

Using z-score formula

x = z* +

= 1.645*2.7 + 70.5

= 74.9

Height denotes the 95th percentile is 74.9