Question

Bob's exam score was 2.17 standard deviations above the mean. the exam was taken by 200 students. assuming a normal distribution, how many scores were higher than bob's?

Answer 1

assuming that it is a normal distribution, then at 2 standard deviation 97.7 % belongs to the distribution and at 3 standard deviation 99.9 % belongs to the group. so to calculate the percentage in 2.17 standard deviation.
(2 - 2.17) / ( 2 - 3) = ( 97.7 - x) / ( 97.7 - 99.9 )
solve for x, which represents the percentage in the 2.17 standard deviations
x = 98.07 %
100 - 98.07 = 1.93 % scores were higher than bob's

Answer 2

The correct answer is:

1.5% of the scores, or 3 people.

Explanation:

A z-score tells the number of standard deviations a data point is from the mean. Since Bob's score is 2.17 standard deviations above the mean, that means his z-score is 2.17.

Using a z-table, we find the probability that a score would be to the left of, or less than, this value. In the table, this is 0.9850. However, we are interested in the number of people that scored higher than Bob. This means we subtract this from 1:

1-0.9850 = 0.015.

This is the percentage of people that scored higher than Bob. To convert to a percent, multiply by 100:

0.015*100 = 1.5.

To find the number of people that scored higher than Bob, take 1.5% of 200:

0.015(200) = 3.