Question

A human resources manager keeps a record of how many years each employee at a large company has been working in their current role. The distribution of these years of experience is strongly skewed to the right with a mean of [3] years and a standard deviation of [2] years. Suppose we were to take a random sample of [4] employees and calculate the sample mean for their years of experience. We can assume independence between members in the sample. What is the probability that the mean years of experience from the sample of [4] employees [bar x] is greater than [3.5] years?

Answer 1

To solve this problem, we can use the Central Limit Theorem and calculate the standard deviation of the sample mean. Then, find the z-score and corresponding probability in the standard normal distribution table.

Step-by-step explanation:

To solve this problem, we can use the Central Limit Theorem, which states that the distribution of sample means will be approximately normal, regardless of the distribution of the population, as long as the sample size is large enough.

First, we need to calculate the standard deviation of the sample mean. The standard deviation of the sample mean, also known as the standard error, is equal to the standard deviation of the population divided by the square root of the sample size.

Using the given values, the standard deviation of the sample mean is 2 divided by the square root of 4, which is 1. Therefore, the probability that the mean years of experience from the sample of 4 employees is greater than 3.5 years can be calculated by finding the z-score of 3.5 using the sample mean and the standard error.

Once we have the z-score, we can look up the corresponding probability in the standard normal distribution table.