Question

hw 3.2: z scores score: 2/6 answered: 1/3 question 2 adult men have heights with a mean of 69.0 inches and a standard deviation of 2.8 inches. find the z - score of a man 64.3 inches tall. (to 2 decimal places) question help: message instructor submit question jump to answer

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 dataset, $\mu$ is the mean, and $\sigma$ is the standard deviation.

Step2: Identify values

We are given that $\mu = 69.0$ inches, $\sigma=2.8$ inches, and $x = 64.3$ inches.

Step3: Substitute values into formula

Substitute the values into the z - score formula: $z=\frac{64.3 - 69.0}{2.8}$
First, calculate the numerator: $64.3-69.0=- 4.7$
Then, divide by the standard deviation: $z=\frac{-4.7}{2.8}\approx - 1.68$

Answer:

-1.68