Problem Number 3

3.) In a recent contest, the mean score was 210 and the standard deviation was 25.

A.) Find the Z score of john who scored 190.

In order to find the Z score, we use the Z formula that we learned in class:

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

We are given a mean score of 210 and a standard deviation of 25 in number 3.

In A we are given our X which is 190. Our X represents John’s score.

We plug the numbers in and solve: 190-210/25=-0.8     —-> remember always follow PEMDAS (parenthesis, exponent, multiplication, division, addition and subtraction.) We subtract 190 -210 first and then divide by 25.


B.) Find the Z score of Bill who scored 270.

Again we are asked to find the Z score. We follow the same formula used in 3a.

Z equals X minus mu divided by standard deviation.

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

Our mean (which is given) is 210 and our standard deviation (also given) is 25

Our X was Bill’s score which was 270.

Now we plug our numbers into the formula:


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


C.) If Mary had a Z-score of 1.25, what was Mary’s score.

Here unlike A and B, we are given Mary’s Z score and are asked to find her X.

In this case, we use the X formula:

X equals mu plus Z times standard deviation


mu=210 (given in original problem)

Standard Deviation=25 (also given in original problem)

When we plug the numbers is we get:


*Here it is important to do PEMDAS as well. First we multiply 1.25(25) and get 31.25 and then we add 210 and get a final answer of 241.25

*I had to write out the formulas because there is no mu symbol nor is there a standard deviation symbol on the computer so here is a picture of the work!

Hope this helped 🙂


2 thoughts on “Problem Number 3

  1. Hey Sarina, I had picked problem # 3 and Professor Reitz mentioned two people aren’t allowed to work on the same problem. So you might want to check in with Prof to see which problem your really suppos to do 🙂

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