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. 0.0703
c. 0.3812
d. 0.1554

Explanation:

Step1: Calculate z - scores

The z - score formula is $z=\frac{x-\mu}{\sigma}$, where $\mu = 200$ (mean), $\sigma = 50$ (standard deviation).
For $x = 170$, $z_1=\frac{170 - 200}{50}=\frac{- 30}{50}=-0.6$.
For $x = 220$, $z_2=\frac{220 - 200}{50}=\frac{20}{50}=0.4$.

Step2: Use the standard normal table

We want to find $P(-0.6$P(-0.6From the standard - normal table, $P(Z < 0.4)=0.6554$ and $P(Z<-0.6)=0.2743$.
So $P(-0.6

Answer:

C. 0.3812