Question

directions: complete the questions below. please show your work! you may use a calculator.

1. womens heights have a mean of 63.6 in. and a standard deviation of 2.5 inches. find the z score corresponding to a woman with a height of 70 inches and interpret it in context.

Explanation:

Step1: Recall z - score formula

The formula for the z - score is $z=\frac{x-\mu}{\sigma}$, where $x$ is the value from the data set, $\mu$ is the mean, and $\sigma$ is the standard deviation.

Step2: Identify values

We are given that $\mu = 63.6$, $\sigma=2.5$, and $x = 70$.

Step3: Calculate z - score

Substitute the values into the formula: $z=\frac{70 - 63.6}{2.5}=\frac{6.4}{2.5}=2.56$.

Step4: Interpret z - score

A z - score of 2.56 means that a woman with a height of 70 inches is 2.56 standard deviations above the mean height of women.

Answer:

The z - score is 2.56. It means the woman's height is 2.56 standard deviations above the mean height of women.