Question

A standardized​ exam's scores are normally distributed. In a recent​ year, the mean test score was 21.4 and the standard deviation was 5.4. The test scores of four students selected at random are 15​, 22​, 9​, and 36. Find the​ z-scores that correspond to each value and determine whether any of the values are unusual.

The z-score for 15 is:

Answer 1

A standardized​ exam's scores are normally distributed. In a recent​ year, the mean test score was 21.4 and the standard deviation was 5.4. The test scores of four students selected at random are 15​, 22​, 9​, and 36. Find the​ z-scores that correspond to each value and determine whether any of the values are unusual.

Answer :

We have given :

μ = population mean = 21.4

σ = population standard deviation = 5.4

We have to find z score for four students selected at random and check it is unusual or not .

## if z score value is below - 3 or  above + 3 then it is unusual .

z score = ( x - mean ) / standard deviation

## The z-score for 15 is :

z = ( 15 - 21.4 ) / 5.4

= - 6.4 / 5.4

= - 1. 1852 ( it is usual , because its value is not below - 3 )

## The z-score for 22  is:

z = ( 22 - 21.4 ) / 5.4

= 0.6  / 5.4

= 0.1111 ( it is usual , because its value is not above   3 )

## The z-score for 9   is:

z = ( 9   - 21.4 ) / 5.4

= - 12.4   / 5.4

= - 2.2963   ( it is usual , because its value is not below - 3 )

## The z-score for 36 is:

z = ( 36 - 21.4 ) / 5.4

= 14.6 / 5.4

= 2.7037 ( it is usual , because its value is not above 3 )

( Here all the z scores value is between -3 to 3 hence there is no unusual value )