Question

The mean of a set of data is -2.14 and its standard deviation is 3.94. Find the z score for a value of 5.40?

Answer 1

`z=1.914`

Explanation:

Given `X` is `"N"(mu=–2.14, sigma = 3.94),` we seek a value `z` such that

`"P"(X<5.40)="P"(Z < z)`

where `Z` has the standard normal distribution of `"N"(0, 1).` In other words, we seek to know how many standard deviations above (or below) the mean our value of 5.40 is in its distribution.

This value is found by "centering" our `x` value (by subtracting `mu`) and then "scaling" it (by dividing that by `sigma`):

`z=(x-mu)/sigma`

`=(5.40-(–2.14))/3.94`

`=1.914`

So our value of `x=5.40` is 1.914 standard deviations above the mean.