Federated South Insurance Company has developed a new screening program for selecting new sales agents. Their past experience indicates that 20% of the new agents hired fail to produce the minimum sales in their first year and are dismissed. Their expectation is that this new screening program will reduce the percentage of failed new agents to 15% or less. If that occurs, they would save $1,000,000 in recruiting and training costs each year. At the end of the first year they want to develop an evaluation to determine if the new program is successful. The following questions are an important part of their research design.
A total of 20 new agents were selected.
a. If this group performs at the same level as past groups, what is the probability 17 or more successfully meet their minimum sales goals in the first year?
b. What is the probability 19 or more reach their minimum sales goals given performance at the same level?
c. If the program has actually increased the probability of success to 0.85 for each new agent, what is the probability that 17 or more meet their minimum sales goals?
d. Given the expected improvement, what is the probability that 19 or more reach their minimum sales goals?