Question

a meteorological office keeps records of the annual precipitation in different cities. for one city, the mean annual precipitation is 24.7 inches and the standard deviation of the annual precipitation amounts is 5.2. let x represent the annual precipitation in that city. determine the z - score for an annual precipitation in that city of 39.6 inches. round your answer to two decimal places.
13.49
−2.87
2.87
1.49

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 $\mu = 24.7$, $\sigma=5.2$, and $x = 39.6$.

Step3: Substitute values into formula

$z=\frac{39.6 - 24.7}{5.2}=\frac{14.9}{5.2}\approx2.87$

Answer:

2.87