Question

1. Compute the z score value for a score of 85 on a test which has a mean of 75 and a standard deviation of 5.

Answer 1

The z-score is 2.

Step-by-step explanation

The z-score for a data set that is normally distributed is calculated using the formula:

`z = (x - \bar x)/( \sigma)`

where

`\bar x`

is the mean and

`\sigma`

is the standard deviation of the distribution.

From the given information the test score is 85.

This implies that,

`x = 85`

The mean is 75.

`\bar x = 75`

The standard deviation is 5.

We substitute the values into the formula to get,

`z = (85 - 75)/(5)`

This implies that

`z = (10)/(5)`

Therefore the z-score is

`z = 2`