The weights of college football players

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.

A) 0.1554 B) 0.3811 C) 0.0703 D) 0.2257

Answer 1

Based on the fact that the weights are normally distributed, we can use the Z statistic and the standard normal probabilities table to compute the probabilities.

To compute the probability the weight is between 170 and 220, we would need to

1) Compute the probability the weight is less than 170.

2) Compute the probability the weight is less than 220.

3) Subtract the probability computed in 1) from the probability computed in 2).

To compute the probability the weight is less than 170 we compute the z-statistic:

z = (x - population mean)/population standard deviation

= (170 - 200)/50 = -0.6

Using the standard normal probabilities table: P(Z < -0.6) = 0.2743

To compute the probability the weight is less than 220 we compute the z-statistic:

z = (220 - 200)/50 = 0.4

Using the standard normal probabilities table: P(Z < 0.4) = 0.6554

The difference of those probabilities = .3811 is the probability the weight is between 170 and 220.