In a qualifying exam for admittance, the mean score was 75 and the standard deviation was 8. 1.) What percent of those who took the qualifying exam got at least 90?

Question

These are additional questions because there's a limit hahah

2.) If there are 150 students who took the qualifying exam, how many students got at least 90?

3.) If 40 students scored between 60 and 75, how many students took the qualifying exam?

Answer 1

For the first part:

This is a z-score problem. For mean 75, SD of 8 and score of 90, we use the Z equation.

Z = (90-75) / 8 = 15/8

P(Z > 15/8) = 0.030396 = 3.03%

Applying this to the next part, out of 150 students, 3.03% of them got at least 90 and that would be about 4 students.

Then for part 3 we have to first compute the probability of scoring between 60 and 75. This is equal to p( less than 75) - p(less than 60).

P(less than 60) is the same as p(greater than 90) = 0.030396.

P(less than 75) = 0.5 since it is just the mean.

So p(between 60 and 75) = 0.5 - 0.03 = 0.47.

Therefore if 40 students got 0.47 of the scores, then we do.

40 = 0.47x

x = 85.1 =85 students total