Question

The heights of male are normally distributed with mean of 170 cm and standard deviation

of 7.5cm. Find the probability that a randomly selected male has a height > 180 cm.

Answer 1

0.0918 = 9.18% probability that a randomly selected male has a height > 180 cm.

Explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean
`\mu` and standard deviation
`\sigma`, the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Mean of 170cm and standard deviation of 7.5 cm.

This means that
`\mu = 170, \sigma = 7.5`

Find the probability that a randomly selected male has a height > 180 cm.

This is 1 subtracted by the pvalue of Z when X = 180. So

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

`Z = (180 - 170)/(7.5)`

`Z = 1.33`

`Z = 1.33` has a pvalue of 0.9082

1 - 0.9082 = 0.0918

0.0918 = 9.18% probability that a randomly selected male has a height > 180 cm.