Question

The weights of college football players are normally distributed with a mean of 200 pounds and a standard deviation of 50 pounds. If a college football player is randomly selected, find the probability that he weighs between 170 and 220 pounds. Round to four decimal places 

A. 0.2257 

B. 0.1554 

C. 0.3812 

D. 0.0703

Answer 1

Given mean
Given mean mu = 200 and sigma = 50 Let X_1 = 170 and X_2 = 220 Z_1 = X_1 - mu/sigma = 170 - 200/50 = - 30/50 = - 0.6 Z_2 = X_2 - mu/sigma = 220 - 200/50 = 20/50 = 0.4 P (170 < X < 220) = P (- 0.6 < Z < 0.4) = P (- 0.6 < Z < 0) + P (0 < Z < 0.4) = P (0 < Z < 0.6) + P (0 < Z < 0.4) (by the symmetry) = 0.2258 + 0.1554 = 0.3812 (c)
and

Let and

  

( by the symmetry )

   $=0.3812$ (c)

Answer 2