Assume that the weights of a male students X is normally dis

Assume that the weights of a male students, X is normally distributed with a mean weight of 160 pounds and standard deviation of 20 pounds.

(a) Out of 1000 men, how many students weigh between 150 and 170 pounds?

(b) Out of 1000 men, how many students weigh more than or exactly 190 pounds?

Solution

(a) P(150<x<170 )

P(-0.5<z<0.5 ) = 0.1915 * 2 = 0.3830

Hence, 0.3830 * 1000 = 383 students out of 1000 weigh between 150 and 170 pounds.

(b) P ( x >=190 )

P ( z >=1.5 ) = 0.5-0.4332 = 0.0668.

Hence, 0.0668 * 1000 = 67 students out of 1000 weigh more than or exactly 190 pounds.