Question

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

Answer 1

Answer:

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

Step-by-step 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:

$Z = \frac{X - \mu}{\sigma}$

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

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{180 - 170}{7.5}$

$Z = 1.33$

$Z = 1.33$ 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.