Question

Assume that the heights of men are normally distributed with a mean of 70.7 inches and a standard deviation of 2.8 inches. If 64 men are randomly selected,

Find:-

(a) Describe the sampling distribution of x. Sketch the distribution.

(b) Find the probability that they have a mean height greater than 71.7 inches.

(c) Find the probability that they have a mean height between 68.5 and 73 inches.

(d) Find the 95th percentile of the heights of men.

Answer 1

Solution :

Given that ,

mean = = 70.7

standard deviation = = 2.8

n = 64

(a)

= / n = 2.8 / 64 = 0.35

(b)

P( > 71.7) = 1 - P( < 71.7)

= 1 - P[( - ) / < (71.7 - 70.7) / 0.35]

= 1 - P(z < 2.86)

= 0.0021

(c)

= P[(68.5 - 70.7) / 0.35 < ( - ) / < (73 - 70.7) / 0.35)]

= P(-6.29 < Z < 6.57)

= P(Z < 6.57) - P(Z < -6.29)

= 1 - 0

= 1

(d)

P(Z < 1.645) = 0.95

z = 1.645

= z * + = 1.645 * 0.35 + 70.7 = 71.28

95th percentile = 71.28