Question

A test score of 48.4 on a test having a mean of 66 and a standard deviation of 11. Find the ​z-score corresponding to the given value and use the ​z-score to determine whether the value is significant. Consider a score to be significant if its ​z-score is less than minus2.00 or greater than 2.00. Round the ​z-score to the nearest tenth if necessary.

Answer 1

The z-score is -1.6 and it is not significant .

Explanation:

Given : Test score = 48.4

Mean = 66

Standard deviation = 11

To Find :Find the ​z-score corresponding to the given value and use the ​z-score to determine whether the value is significant.

Solution:

Formula :
`z=(x-\mu)/(\sigma)`

`\mu =66\\x=48.4\\\sigma =11`

Substitute the values

`z=(48.4-66)/(11)`

`z=-1.6`

So, the z-score is -1.6

Now we are given that Consider a score to be significant if its ​z-score is less than -2.00 or greater than 2.00.

Since -1.6>-2 and -1.6<2

So, It is not significant

Hence the z-score is -1.6 and it is not significant .