Discuss the below:
Q: In a typical month, an insurance agent presents life insurance plans to 40 potential customers. Historically, one in four such customers chooses to buy life insurance from this agent. Based on the relevant binomial distribution, response the following questions;
a) What is the probability that exactly 5 customers will buy life insurance from this agent in the coming month?
b)What is the probability that no more than 10 customers will buy life insurance from this agent in the coming month?
c)What is the probability that at least 20 customers will buy life insurance from this agent in the coming month?
| Life insurance sales |
|
|
|
| Number of trials |
100 |
| P(success) on each trial |
0.1 |
|
|
| Part (a) |
|
| P(5 successes) |
0.0339 |
|
|
| Part (b) |
|
| P(<=10 successes) |
0.5832 |
|
|
| Part (c ) |
|
| P(>=20 successes) |
0.0020 |
|
|
| Part (d) |
|
| Mean |
10 |
| Stdev |
3.0000 |
|
|
| Part (e) |
|
| Mean - 2*stdev |
4.0000 |
| Mean + 2*stdev |
16.0000 |
| P(between 5 and 15 inclusive) |
0.9364 |
|
|
| Part (f) |
|
| Mean - 3*stdev |
1.0000 |
| Mean + 3*stdev |
19.0000 |
| P(between 2 and 18 inclusive) |
0.9951 |