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)0.2257
D)0.0703

Question

Quizplus · Accepted Answer

To find the probability that a player weighs between 170 and 220 pounds, we use the Z-score formula: Z = (X - μ) / σ, where X is the value, μ is the mean, and σ is the standard deviation. For X = 170, Z = (170 - 200) / 50 = -0.6. For X = 220, Z = (220 - 200) / 50 = 0.4. Looking these Z-scores up in a standard normal distribution table or using a calculator, we find the probabilities for Z = -0.6 and Z = 0.4, then subtract the smaller from the larger to find the probability of being between these two Z-scores. This calculation gives us approximately 0.3811, indicating the probability a randomly selected player weighs between 170 and 220 pounds.

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