Question

1)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. You may treat this as a binomial experiment.

What is the probability of success?

What is the total number of trials?

Create a probability distribution table which includes probability of each possible outcome. Also create the cumulative probability column.

What is the probability that exactly five customers will buy life insurance from this agent in the coming month?

What is the probability that no more than 10 customers will buy life insurance from this agent in the coming month?

What is the probability that at least 20 customers will buy life insurance from this agent in the coming month?

Determine the mean and standard deviation of the number of customers who will buy life insurance from this agent in the coming month?

What is the probability that the number of customers who buy life insurance from this agent in the coming month will lie within two standard deviations of the mean?

Answer 1

What is the probability of success?

1/4 = 0.25

What is the total number of trials?

40

Create a probability distribution table which includes probability of each possible outcome. Also create the cumulative probability column.

	40	n
	0.25	p
		cumulative
X	P(X)	probability
0	0.00001	0.00001
1	0.00013	0.00014
2	0.00087	0.00102
3	0.00368	0.00470
4	0.01135	0.01604
5	0.02723	0.04327
6	0.05295	0.09622
7	0.08573	0.18195
8	0.11788	0.29983
9	0.13971	0.43954
10	0.14436	0.58390
11	0.13124	0.71514
12	0.10572	0.82087
13	0.07590	0.89677
14	0.04879	0.94556
15	0.02819	0.97376
16	0.01468	0.98844
17	0.00691	0.99535
18	0.00294	0.99829
19	0.00114	0.99943
20	0.00040	0.99983
21	0.00013	0.99995
22	0.00004	0.99999
23	0.00001	1.00000
24	0.00000	1.00000
25	0.00000	1.00000
26	0.00000	1.00000
27	0.00000	1.00000
28	0.00000	1.00000
29	0.00000	1.00000
30	0.00000	1.00000
31	0.00000	1.00000
32	0.00000	1.00000
33	0.00000	1.00000
34	0.00000	1.00000
35	0.00000	1.00000
36	0.00000	1.00000
37	0.00000	1.00000
38	0.00000	1.00000
39	0.00000	1.00000
40	0.00000	1.00000
	1.00000
	10.000	expected value
	7.500	variance
	2.739	standard deviation

What is the probability that exactly five customers will buy life insurance from this agent in the coming month?

0.02723

What is the probability that no more than 10 customers will buy life insurance from this agent in the coming month?

0.58390

What is the probability that at least 20 customers will buy life insurance from this agent in the coming month?

0.00057

Determine the mean and standard deviation of the number of customers who will buy life insurance from this agent in the coming month?

Mean = 10

Standard deviation = 2.739

What is the probability that the number of customers who buy life insurance from this agent in the coming month will lie within two standard deviations of the mean?

0.9545