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

Question

Quizplus · Accepted Answer

To find the probability that the player weighs between 170 and 220 pounds, we need to find the area under the normal curve between those two values. We can standardize the distribution by using the z-score formula:

z = (x - μ) / σ

Where x is the weight we are interested in, μ is the mean weight, and σ is the standard deviation.

For x = 170:

z = (170 - 200) / 50 = -0.6

For x = 220:

z = (220 - 200) / 50 = 0.4

Now we can use a standard normal distribution table (or a calculator that has this function) to find the area under the curve between these two z-scores. The answer is:

P(-0.6 < z < 0.4) = 0.3811

Therefore, the best choice is B.

The Weights of College Football Players Are Normally Distributed with a Mean