A local realestate company invests in retirement accounts fo

A local real-estate company invests in retirement accounts for all full-time employees. The company automatically deposits an amount equal to 3% of the employee’s base salary into a 401K account through an investment firm. Employees of the company may choose to have a portion of their pay deposited into these accounts as well, but they are not required to do so.

The company has access to the annual return rate data on all 254 of their employee’s accounts for the 2014-2015 fiscal year. They have analyzed the data, and found that it is approximately normally distributed with a mean annual return rate of 6.71% and standard deviation of 2.93%. Finally, they know that 82, or 32%, of all their full-time employees did not choose to deposit a portion of their pay into these accounts.

Let X = the annual rate return rate of a company employee (%).

Let Y = the choice to deposit a portion of an their pay into the retirement account (Yes=0 or No=1)

Suppose we are going to randomly select a group of 40 employees. what is the probability that at most 18 employees in the sample choose not to deposit a portion of their pay into their company retirement account?

Solution

Using a cumulative hypergeometric distribution table or technology, matching          
          
where          
N = population size =    254      
K = number of successes in the population =    82      
n = sample size =    40      
x = critical number of successes in the sample =    18      
  

Thus,

P(at most   18   ) =    0.978463773 [ANSWER]