Question

My friend, let's call her Pam, took the same history course I did, but we had different professors. On the final exam, I scored 82 out of 100 points while she scored 47 out of 63 points. My percent score, 82%, is greater than her percent score, which is about 75%. So I think I did better than she did on the final exam. But she tells me that both sets of scores are normally distributed and that I have to look at the standard scores to find out who did better. Pam tells me that the mean and standard deviation for my test are 76.1 and 6.5, respectively, while hers are 40 and 4.2 respectively, so if I "do the math," then I should see why she performed better. Can you please explain what she means by standard scores and can you "do the math" that she mentions. Yours, Confused History Buff P.S. If she did perform better, I have to buy her dinner!

Answer 1

Explanation:

Dear Pam,

I understand your confusion about standard scores and how they can determine who performed better on the final exam. Standard scores, also known as z-scores, allow us to compare scores from different distributions by converting them into a common scale.

To calculate the z-score, we use the formula: z = (x - mean) / standard deviation, where x represents the score you want to convert.

Let's calculate the z-scores for both your and Pam's scores:

For your score of 82:

z = (82 - 76.1) / 6.5 = 0.908

For Pam's score of 47:

z = (47 - 40) / 4.2 = 1.667

Now, comparing the z-scores, we can determine who performed better. A higher z-score indicates a better performance relative to the mean. In this case, your z-score of 0.908 is higher than Pam's z-score of 1.667. Therefore, you performed better on the final exam.

I hope this explanation helps clear up your confusion. If you have any further questions, feel free to ask!

Best Regards

[Your Name]

Hope this helps.

Answer 2

Answer: To calculate the standard score, also known as the z-score, we can use the following formula:

z = (x - mean) / standard deviation

1. For your test score:

- Mean: 76.1

- Standard deviation: 6.5

- Your score: 82

Plug these values into the formula:

z = (82 - 76.1) / 6.5

2. For your friend's test score:

- Mean: 40

- Standard deviation: 4.2

- Your friend's score: 47

Plug these values into the formula:

z = (47 - 40) / 4.2

Calculating these values will give us the z-scores for both you and your friend, indicating how many standard deviations your scores are from their respective means.

By comparing the z-scores, we can determine who performed relatively better on the exam. A higher z-score indicates a better performance relative to the mean of the distribution.

Once you have calculated the z-scores, you can compare them to see which one is higher. The higher z-score indicates a relatively better performance on the exam.

So, by "doing the math" and calculating the z-scores, you can determine who performed better on the final exam. If your z-score is higher than your friend's, it means you performed better, and you won't have to buy her dinner! ps, sorry for the long responce