Question

Two of your friends each received the results of their first midterm exam this term. Andy's score on the Spanish exam was 22.5 points. The distribution of Spanish exam scores was normal (bell-shaped) with an average score of 20 points (out of 25 points possible) and a standard deviation of 1.97 points. Jennifer's score the the math exam was 72 points. The distribution of math exam scores was uniform over the range of 20 to 80 points, with a mean of 50 points and a standard deviation of 17.32 points.Over dinner your friends begin discussing their results, each claiming they did better on their exam. They remember you are taking Stats 250 this term and turn to you for help to resolve the question: Who did better on their midterm exam?

Answer 1

Jennifer has the higher zscore, so she did better than Andy on the midterm exam.

Explanation:

Problems of normally distributed samples can be solved using the zscore.

The z-score formula is given by:

`Z = (X - \mu)/(\sigma)`

In which: X is the grade,
`\mu` is the mean value of all the grades and
`\sigma` is the standard deviation of the grades.

Between Andy and Jennifer, whoever has the highest Zscore did better on their midterm exam.

Andy:

Andy's score on the Spanish exam was 22.5 points. The distribution of Spanish exam scores was normal (bell-shaped) with an average score of 20 points (out of 25 points possible) and a standard deviation of 1.97 points. So
`X = 22.5, \mu = 20, \sigma = 1.97`

`Z = (X - \mu)/(\sigma)`

`Z = (22.5 - 20)/(1.97)`

`Z = 1.269`

Jennifer

Jennifer's score the the math exam was 72 points. The distribution of math exam scores was uniform over the range of 20 to 80 points, with a mean of 50 points and a standard deviation of 17.32 points. So
`X = 72, \mu = 50, \sigma = 17.32`

`Z = (X - \mu)/(\sigma)`

`Z = (72 - 50)/(17.32)`

`Z = 1.2702`

Jennifer has the higher zscore, so she did better than Andy on the midterm exam.