A final exam in Math 160 has a mean of 73 with standard deviation 7.8. If 24 students are randomly selected, find the probability that the mean of their test scores is greater than 78.
A) 0.8962
B) 0.0036
C) 0.0103
D) 0.0008

Question

Quizplus · Accepted Answer

The sampling distribution of the sample mean will have a mean of 73 and a standard deviation of 7.8/sqrt(24). To find the probability that the sample mean is greater than 78, calculate the z-score and use the standard normal distribution. The z-score is (78-73)/(7.8/sqrt(24)) ≈ 3.06. The probability of a z-score greater than 3.06 is approximately 0.0008.

A Final Exam in Math 160 Has a Mean of 73