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In a typical month, an insurance agent presents life insurance plans to 40 potential customers. Historically,...

  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.
    1. What is the probability of success for this problem?
    2. What is the total number of trials in this problem?
    3. Create a probability distribution table which includes the value for the random variable and the probability of each possible outcome of the random variable. Also create the cumulative probability column.
    4. What is the probability that exactly five customers will buy life insurance from this agent in the coming month?
    5. What is the probability that no more than 10 customers will buy life insurance from this agent in the coming month?
    6. What is the probability that at least 20 customers will buy life insurance from this agent in the coming month?
    7. Determine the mean and standard deviation of the number of customers who will buy life insurance from this agent in the coming month?
    8. 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?

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Solutions

Expert Solution

x P(X=x) F(x)
0 1.00566E-05 1.00566E-05
1 0.000134088 0.000144144
2 0.000871571 0.001015715
3 0.003679965 0.00469568
4 0.011346559 0.01604224
5 0.027231743 0.043273983
6 0.052950611 0.096224593
7 0.085729561 0.181954154
8 0.117878146 0.2998323
9 0.139707432 0.439539732
10 0.144364346 0.583904078
11 0.131240315 0.715144393
12 0.105721365 0.820865758
13 0.075902518 0.896768276
14 0.048794476 0.945562752
15 0.028192364 0.973755116
16 0.014683523 0.988438639
17 0.006909893 0.995348532
18 0.002943103 0.998291635
19 0.001135934 0.999427569
20 0.000397577 0.999825146
21 0.000126215 0.999951361
22 3.63346E-05 0.999987695
23 9.47859E-06 0.999997174
24 2.238E-06 0.999999412
25 4.7744E-07 0.999999889
26 9.18154E-08 0.999999981
27 1.58693E-08 0.999999997
28 2.45597E-09 1
29 3.38754E-10 1
30 4.14033E-11 1
31 4.45197E-12 1
32 4.17372E-13 1
33 3.3727E-14 1
34 2.3146E-15 1
35 1.32263E-16 1
36 6.12328E-18 1
37 2.20659E-19 1
38 5.80681E-21 1
39 9.92617E-23 1
40 8.27181E-25 1

milcah answered 1 year ago
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