# Lesson 6 the central limit theorem

### Lesson 6

### The Central Limit Theorem

Consider the following scenario and answer the 4 questions which follow.

Human Resource Consulting (HRC) surveyed a random sample of 60 Twin Cities construction companies to find information on the costs of their health care plans. One of the items being tracked is the annual deductible that employees must pay. The Minnesota Department of Labor reports that historically the mean deductible amount per employee is $502 with a standard deviation of $100.

1. Compute the standard error of the sample mean for HRC.

2. What is the chance HRC finds a sample mean between $477 and $527?

3. Calculate the likelihood that the sample mean is between $492 and $512.

4. What is the probability the sample mean is greater than $550?

**Grading: ***Each part is worth 25 points.*