Bob made 116 on his accounting midterm and 82 on his biology midterm. For the accounting midterm, the mean score was 102 with standard deviation 14. For the biology midterm, the mean score was 70 with standard deviation of 5. Which score was the higher with respect to the rest of the class? Explain your answer.

Question

Bob made 116 on his accounting midterm and 82 on his biology midterm. For the accounting midterm, the mean score was 102 with standard deviation 14. For the biology midterm, the mean score was 70 with standard deviation of 5. Which score was the higher with respect to the rest of the class? Explain your answer.

Answer 1

his accounting score was one s.d. above the mean ... 84th percentile

... while his bio score was 2.4 s.d. above the mean ... 99th percentile

the percentiles are from the z-score table

Answer 2

To determine which score is higher with respect to the rest of the class, we need to compare Bob's scores to the mean and standard deviation of each class.

Let's start with the accounting midterm. Bob scored 116, and the mean score for the class is 102, with a standard deviation of 14.

To see how Bob's score compares to the rest of the class, we can calculate his z-score using the formula:

z = (x - μ) / σ

where:
- x is the individual score (116 in this case)
- μ is the mean score of the class (102)
- σ is the standard deviation of the class (14)

Plugging in the values, we get:

z = (116 - 102) / 14
z = 14 / 14
z = 1

Bob's z-score for the accounting midterm is 1. This means that his score is 1 standard deviation above the mean.

Now let's move on to the biology midterm. Bob scored 82, and the mean score for the class is 70, with a standard deviation of 5.

Using the same formula, we can calculate his z-score for the biology midterm:

z = (x - μ) / σ

Plugging in the values, we get:

z = (82 - 70) / 5
z = 12 / 5
z = 2.4

Bob's z-score for the biology midterm is 2.4. This means that his score is 2.4 standard deviations above the mean.

Comparing the two z-scores, we can see that Bob's z-score for the biology midterm (2.4) is higher than his z-score for the accounting midterm (1). This means that Bob's score of 82 on the biology midterm is relatively higher with respect to the rest of the class compared to his score of 116 on the accounting midterm.

Therefore, Bob's score of 82 on the biology midterm was higher with respect to the rest of the class.