8.) The mean score on a Statistics exam was 82, with a standard deviation of 6. Find the standard score (z-score) for each of the students below.

- A.) Alice’s score was 94.

In order to find the Z score, we use the Z formula. This formula is:

Z equals X minus MU (mu is the same as the mean) divided by standard deviation.

We are given a mean score of 82 and a standard deviation of 6.

Our X is also given as Alice’s score of 94.

We now plug the numbers in and solve:

94-82/6

*Remember always follow PEMDAS (parenthesis, exponent, multiplication, division, addition and subtraction.)

94-82=12

12/6=2

Alice’s Z score is: **2**

- B.) Bob’s score was 76.

To find Bob’s Z score we use the Z formula as well.

Z equals X minus mu (mu is the same as the mean) divided by standard deviation.

Here our mean and standard deviation are the same but our X is different.

Our mean (which is given) is 82 and our standard deviation (also given) is 6.

Our X is Bob’s score which is 76.

Now we plug our numbers into the formula:

76-82/6

Here PEMDAS should also be used which means we subtract before we divide.

76-82=-6

-6/6=-**1**

- C.) Charlie’s score was 98.

To find Charlie’s Z score we use the Z formula as well.

Z equals X minus mu (mu is the same as the mean) divided by standard deviation.

Here our mean and standard deviation are the same but our X is different.

Our mean (which is given) is 82 and our standard deviation (also given) is 6.

Our X is Charlie’s score which is 98.

Now we plug our numbers into the formula:

98-82/6

Here PEMDAS should also be used which means we subtract before we divide.

98-82=16

16/6=**2.67**

**Here is a picture of the work:**