The MBA program at Dover College has an enrollment of 160 students with an average age of 34.7 years old and a standard deviation 5.2 years. A random sample of 40 MBA students was selected. What is the probability that the average age of the sample is less than 34 years old?
A)0.3300
B)0.1635
C)0.2946
D)0.4443

Question

Quizplus · Accepted Answer

To find the probability that the average age of the sample is less than 34 years old, we use the formula for the z-score in a sampling distribution: $ z = \frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}}} $, where $\bar{x}$ is the sample mean (34 years), $\mu$ is the population mean (34.7 years), $\sigma$ is the population standard deviation (5.2 years), and $n$ is the sample size (40). Plugging in the values, we get $ z = \frac{34 - 34.7}{\frac{5.2}{\sqrt{40}}} $. This calculation gives us a z-score, which we then look up in a standard normal distribution table to find the corresponding probability. The calculated z-score corresponds to a probability of 0.1635, indicating the likelihood that the sample mean is less than 34 years old.

The MBA Program at Dover College Has an Enrollment of 160