Question

Suppose the systolic blood pressure of an adult male is normally distributed with a mean of 138 mm of mercury and standard deviation of 10. If an adult male is picked at random, find the probability that his systolic blood pressure will be… a. Greater than 160 mm

Answer 1

Using the normal distribution, it is found that there is a 0.0139 = 1.39% probability that his systolic blood pressure will be greater than 160 mm.

Normal Probability Distribution

In a normal distribution with mean $\mu$ and standard deviation $\sigma$, the z-score of a measure X is given by:

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

• It 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, which is the percentile of X.

In this problem:

• The mean is of 138 mm, hence $\mu = 138$.

• The standard deviation is of 10 mm, hence $\sigma = 10$.

The probability that his systolic blood pressure will be greater than 160 mm is 1 subtracted by the p-value of Z when X = 160, hence:

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

$Z = \frac{160 - 138}{10}$

$Z = 2.2$

$Z = 2.2$ has a p-value of 0.9861.

1 - 0.9861 = 0.0139

0.0139 = 1.39% probability that his systolic blood pressure will be greater than 160 mm.

You can learn more about the normal distribution at https://brainly.com/question/24663213