Question

The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds. The probability of a player weighing more than 250 pounds is Group of answer choices 0.9505 0.9772 0.0228 0.4505 0.0495

Answer 1

0.0228

Explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean
`\mu` and standard deviation
`\sigma`, the zscore of a measure X is given by:

`Z = (X - \mu)/(\sigma)`

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds.

This means that
`\mu = 200, \sigma = 25`

The probability of a player weighing more than 250 pounds is

This is 1 subtracted by the pvalue of Z when X = 250. So

`Z = (X - \mu)/(\sigma)`

`Z = (250 - 200)/(25)`

`Z = 2`

`Z = 2` has a pvalue of 0.9772

1 - 0.9772 = 0.0228

The probability of a player weighing more than 250 pounds is 0.0228