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 greater than 71.
A)0.8962
B)0.0008
C)0.5036
D)0.9012

Question

Quizplus · Accepted Answer

Using the Central Limit Theorem, we can calculate the probability that the mean of their test scores is greater than 71. 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: $z = \frac{71 - 73}{\frac{7.8}{\sqrt{24}}}$. This calculation gives a z-score, which can then be used to find the probability from the standard normal distribution table or a calculator. The result corresponds to the probability of 0.8962, indicating that there's an 89.62% chance the mean of their test scores is greater than 71.

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