The average score of 100 students taking a statistics final was 70 with a standard deviation of 7. Assuming a normal distribution,what test score separates the top 25% of the students from the lower 75% of students?
A)70.00
B)74.69
C)65.31
D)75.25

Question

Quizplus · Accepted Answer

We can use the z-score formula to find the test score that separates the top 25% from the lower 75%:

z = (x - μ) / σ

where x is the test score we want to find, μ is the mean (70), and σ is the standard deviation (7).

To find the z-score that corresponds to the top 25%, we look up the z-score that corresponds to a cumulative area of 0.75 in a standard normal table. This is approximately 0.67.

So we can set up the equation:

0.67 = (x - 70) / 7

Solving for x, we get:

x = 74.69

Therefore, the test score that separates the top 25% of the students from the lower 75% is approximately 74.69.

The Average Score of 100 Students Taking a Statistics Final