Question

Make Excel do all calculations, using cell addresses. Don’t type numbers in your formulas.

Report the answers to the questions in your worksheet using the appropriate symbols (µ σ) and notation p(x>=5), p(X<3) etc...

            Use Insert/Symbol to find mu and sigma for mean and std dev.

                                   

x	P(x)

1. An auditor for Health Maintenance Services of Georgia reports 30 percent of policyholders 55 years or older submit a claim during the year. Twelve policyholders are randomly selected for company records.

a. What type of distribution is this likely to be?

b. What is the expected number (mean) of the distribution?

c. What is the standard deviation of the distribution?

Use the tables in your text to answer the following questions

d. What is the probability that exactly 6 of the 12 policyholders have filed a claim?

e. What is the probability that more than 6 of the 12 policyholders have filed a claim?

f. What is the probability that 6 or fewer of the 12 policyholders have filed a claim?

g. What is the probability that at least 6 of the 12 policyholders have filed a claim?

Use the BINOMDIST function to answer the following questions

h. What is the probability that exactly 8 of the 12 policyholders have filed a claim?

i. What is the probability that more than 8 of the 12 policyholders have filed a claim?

j. What is the probability that 8 or fewer of the 12 policyholders have filed a claim?

k. What is the probability that at least 8 of the 12 policyholders have filed a claim?

Answer 1

1. a) Binomial distribution is suitable to the given data. The parameters n = 12 and p = 0.30

The probability mass function is

x	P(X=x)
0	0.013841287
1	0.071183763
2	0.167790298
3	0.239700426
4	0.231139696
5	0.158495792
6	0.079247896
7	0.029111472
8	0.007797716
9	0.001485279
10	0.000190964
11	0.0000149
12	0.0000005

b) From the probability distribution is

x	P(x)	xP(X=x)	X^2P(X=x)
0	0.0138413	0.0000	0.0000
1	0.0711838	0.0712	0.0712
2	0.1677903	0.3356	0.6712
3	0.2397004	0.7191	2.1573
4	0.2311397	0.9246	3.6982
5	0.1584958	0.7925	3.9624
6	0.0792479	0.4755	2.8529
7	0.0291115	0.2038	1.4265
8	0.0077977	0.0624	0.4991
9	0.0014853	0.0134	0.1203
10	0.0001910	0.0019	0.0191
11	0.0000149	0.0002	0.0018
12	0.0000005	0.0000	0.0001
Total:		3.6	15.48

Use the tables in your text to answer the following questions

d. The probability that exactly 6 of the 12 policyholders have filed a claim is 0.0792479

e. The probability that more than 6 of the 12 policyholders have filed a claim is 0.0386

f. The probability that 6 or fewer of the 12 policyholders have filed a claim is 1 - 0.0386 = 0.9614

g. The probability that at least 6 of the 12 policyholders have filed a claim is 0.1178

Use the BINOMDIST function to answer the following questions