Solve the problem.
-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 less than 70.
A) 0.1006
B) 0.9699
C) 0.0301
D) 0.0278

Question

Quizplus · Accepted Answer

First, we need to standardize the sample mean using the formula:
z = (x - μ)/(σ/√n)
where x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.

Substituting the given values, we get:
z = (70 - 73)/(7.8/√24) = -1.78

Next, we need to find the probability that the standardized sample mean is less than -1.78. Using a standard normal table or calculator, we find:
P(z < -1.78) = 0.0301

Therefore, the answer is C.

Solve the Problem. -A Final Exam in Math 160 Has a Mean of a Mean