The average score of 100 students taking a statistics final was 70 with a standard deviation of 7. Assuming a normal distribution,what is the probability that a student scored greater than 65?
A)0.2611
B)0.2389
C)0.7611
D)−0.714

Question

Quizplus · Accepted Answer

Using the Z-score formula, Z = (X - μ) / σ, where X is the score (65), μ is the mean (70), and σ is the standard deviation (7), we find Z = (65 - 70) / 7 = -0.714. Looking up this Z-score in a standard normal distribution table or using a calculator, we find the probability of scoring less than 65 is approximately 0.2389. Therefore, the probability of scoring greater than 65 is 1 - 0.2389 = 0.7611.

The Average Score of 100 Students Taking a Statistics Final