Question

If a normal distribution has a mean of 132 and a standard deviation of 20 what is the value that has a z score of 2.4?

Answer 1

The value that has a z score of 2.4 is 180.

Explanation:

Given : If a normal distribution has a mean of 132 and a standard deviation of 20.

To find : What is the value that has a z score of 2.4?

Solution :

The formula of z-score is given by

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

where, z=2.4 is z score value

`\mu=132` is the mean of the normal distribution

`\sigma=20` is the standard deviation

x is the value of z score.

Substituting all the values in the formula,

`2.4=(x-132)/(20)`

`2.4* 20=x-132`

`48=x-132`

`x=180`

Therefore, The value that has a z score of 2.4 is 180.

Answer 2

The value is 180

Explanation:

The formula for z score is given by

x - mean

z= -------------

standard deviation

We know z= 2.4

We know the standard deviation =20

and we know the mean = 132

We can find x

x - 132

2.4 = ----------------

20

Multiply each side by 20

2.4 *20 = x-132

48 = x-132

Add 132 to each side

48+132 = x -132+132

180 = x