The average score of 100 students taking a statistics final was 70 with a standard deviation of 7. Assuming a normal distribution, approximately how many scored greater than 65?
A) 0.2611
B) 0.2389
C) 0.7611
D) D)-0.714
E) None of the choices are correct

Question

Quizplus · Accepted Answer

Using the Z-score formula, Z = (X - μ) / σ, where X = 65, μ = 70, and σ = 7, we find Z = (65 - 70) / 7 = -0.714. The cumulative probability for Z = -0.714 is approximately 0.2389, so the probability of scoring greater than 65 is 1 - 0.2389 = 0.7611. Thus, approximately 76.11% of students scored greater than 65.

The Average Score of 100 Students Taking a Statistics Final