Question

The average weight of men between the ages of 40-49 is 202.3 pounds with a standard deviation of 50.7 pounds. Find the probability that a man in this age group is under 180 pounds if it is known that the distribution is approximately normal. Group of answer choices

Answer 1

33% probability that a man in this age group is under 180 pounds

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.

In this question:

`\mu = 202.3, \sigma = 50.7`

Find the probability that a man in this age group is under 180 pounds if it is known that the distribution is approximately normal.

This is the pvalue of Z when X = 180.

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

`Z = (180 - 202.3)/(50.7)`

`Z = -0.44`

`Z = -0.44` has a pvalue of 0.33

33% probability that a man in this age group is under 180 pounds