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

Answer:

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

Step-by-step 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

$z=\frac{x-\mu}{\sigma}$

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,

$2.4=\frac{x-132}{20}$

$2.4\times 20=x-132$

$48=x-132$

$x=180$

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

Answer 2

Answer:

The value is 180

Step-by-step 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