Question

If a normal distribution has a mean of 154 and a standard deviation of 15, what is the value that has a z-score of 2.2?

a. 166
b. 196
c. 187
d. 208

Answer 1

Option c. is correct

Explanation:

The standard deviation is a measure of the amount of dispersion in a set of values.

Mean of a normal distribution (m) = 154

Standard deviation (s) = 15

z-score = 2.2

To find: value (x) that has a z-score of 2.2

z-score is given by
`z=(x-m)/(s)`

Put
`z=2.2,.m=154,s=15`

`2.2=(x-154)/(15)\\15(2.2)=x-154\\33=x-154\\x=33+154\\=187`

Option c.is correct