Question

The z-score tells you how many standard deviations about the mean a given data value is. Find the z-score in this situation:

A group of bats has a mean weight of 15 grams with a standard deviation of 1.6 grams. What is the z-score of Carl the bat who weighs 17.2 grams?

Show your work or explain what you did, and write your answer rounded to two decimal places as you would need to do for use in the standard normal table.

Answer 1

1.standard deviations

2.mean

Explanation:

Answer 2

Z-score = -1.38

Explanation:

The z-score measures how many standard deviations from the mean a data is

Therefore the z score is the quotient between the difference between a value and the mean and the standard deviation

`Z =(X-\mu)/(\sigma)`

Where

μ is the mean, x is a data of the population and
`\sigma` is the standard deviation

In this case

`\mu = 15\ g\\\\\sigma = 1.6\ g\\\\X = 17.2\ g`

Then the z-score is

`Z = (15-17.2)/(1.6)\\\\Z = -1.38`