Question

A company, United Consumers, is considering the option of replacing its employer provided insurance plan with what is known as Consumer Directed Health Plan (CDHP). Under this new plan, the company would provide its employees with a sum of money so that the employees can purchase their health plan form the online marketplace. This plan is based on the belief that employees tend to behave more responsibly if they have to spend their own money as consumers. According to a recent study, a market research firm found that generally 41% of the employees (who had the option to choose CDHP) chose CDHP as their choice over their traditional employer sponsored plan. The company, United Consumers, employs 290 people. In order to find out the acceptance of CDHP among its employees, a random sample of 40 employees was selected. Compute the following based on this information:

- What is the probability that 18 or more employees from this sample chose CDHP as their choice?

- What is the probability that between 17 and 22 employees from this sample chose CDHP as their choice?

Answer 1

We have used the fact that if X is a Binomial random variable and we have large sample size then X can be approximated as a normal random variable.   Generally for n>= 30 we can do it.