Question

According to a study done by UCB students, the height for Martian adult males is normally distributed with an average of 65 inches and a standard deviation of 2.3 inches. Suppose one Martian adult male is randomly chosen. Let X = height of the individual. Round all answers to 3 decimal places where possible.

a. What is the distribution of X? X ~ N 65, 2.3

b. Find the probability that the person is between 60.2 and 62.1 inches. 0.0852

c. The middle 40% of Martian heights lie between what two numbers?

Answer 1

a) The distribution of X is normal.

b) P(60.2 < X < 62.1)

= P((60.2 - )/ < (X - )/ < (62.1 - )/)

= P((60.2 - 65)/2.3 < Z < (62.1 - 65)/2.3)

= P(-2.09 < Z < -1.26)

= P(Z < -1.26) - P(Z < -2.09)

= 0.1038 - 0.0183

= 0.0855 = 0.086

c) P(X < x) = 0.3

or, P((X - )/ < (x - )/) = 0.3

or, P(Z < (x - 65)/2.3) = 0.3

or, (x - 65)/2.3 = -0.52

or, x = -0.52 * 2.3 + 65

or, x = 63.804

P(X > x) = 0.3

or, P((X - )/ > (x - )/) = 0.3

or, P(Z > (x - 65)/2.3) = 0.3

or, P(Z < (x - 65)/2.3) = 0.7

or, (x - 65)/2.3 = 0.52

or, x = 0.52 * 2.3 + 65

or, x = 66.196