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 78.
A)0.0036
B)0.0008
C)0.8962
D)0.0103

Question

Quizplus · Accepted Answer

To find the probability that the mean of their test scores is greater than 78, we use the formula for the standard error of the mean: $\sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}}$, where $\sigma$ is the population standard deviation and $n$ is the sample size. Here, $\sigma = 7.8$ and $n = 24$, so $\sigma_{\bar{x}} = \frac{7.8}{\sqrt{24}}$. Then, we calculate the z-score for a mean of 78: $z = \frac{\bar{x} - \mu}{\sigma_{\bar{x}}}$, where $\bar{x} = 78$ and $\mu = 73$. Plugging in the values, we find the z-score and then use the standard normal distribution to find the probability corresponding to this z-score. The calculation leads to a very small probability, which matches closest to choice B, indicating a rare event.

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