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)0.9699
B)0.0301
C)0.1006
D)0.0278

Question

Quizplus · Accepted Answer

Using the Central Limit Theorem, we can calculate the probability that the mean of a sample is less than a certain value. The formula for the z-score in this context is $z = \frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}}}$, where $\bar{x}$ is the sample mean, $\mu$ is the population mean, $\sigma$ is the population standard deviation, and $n$ is the sample size. Plugging in the given values: $z = \frac{70 - 73}{\frac{7.8}{\sqrt{24}}}$. This gives a z-score, which can then be looked up in a standard normal distribution table or calculated using a calculator to find the probability. The correct probability associated with the calculated z-score is 0.0301, indicating a small chance that the sample mean is less than 70.

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