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# Binomial & Poisson Probabilities

5.2 Determine the mean, the variance, and the standard deviation of the following discrete distribution.
x P( x)
0 .103
1 .118
2 .246
3 .229
4 .138
5 .094
6 .071
7 .001

5.6 Problems

Solve the following problems by using the binomial tables ( Appendix A Below).

a. If n = 20 and p = .50, find P ( x = 12).
d. If n = 20 and p = .90, find P ( x = 16).

5.10 Problem

The Wall Street Journal reported some interesting statistics on the job market. One statistic is that 40% of all workers say they would change jobs for " slightly higher pay." In addition, 88% of companies say that there is a shortage of qualified job candidates. Suppose 16 workers are randomly selected and asked if they would change jobs for " slightly higher pay." What is the probability that nine or more say yes? What is the probability that three, four, five, or six say yes? If 13 companies are contacted, what is the probability that exactly 10 say there is a shortage of qualified job candidates? What is the probability that all of the companies say there is a shortage of qualified job candidates? What is the expected number of companies that would say there is a shortage of qualified job candidates?

5.16 a-d Problems

Find the following values by using the Poisson tables in Appendix A below

A. P ( x = 6| . = 3.8)
D. P ( x = 0| . = 1.9)

Appendix A
x .1 .2 .3 .4 .5 .6 .7 .8 .9
0 .122 .012 .001 .000 .000 .000 .000 .000 .000
1 .270 .058 .007 .000 .000 .000 .000 .000 .000
2 .285 .137 .028 .003 .000 .000 .000 .000 .000
3 .190 .205 .072 .012 .001 .000 .000 .000 .000
4 .090 .218 .130 .035 .005 .000 .000 .000 .000
5 .032 .175 .179 .075 .015 .001 .000 .000 .000
6 .009 .109 .192 .124 .037 .005 .000 .000 .000
7 .002 .055 .164 .166 .074 .015 .001 .000 .000
8 .000 .022 .114 .180 .120 .035 .004 .000 .000
9 .000 .007 .065 .160 .160 .071 .012 .000 .000
10 .000 .002 .031 .117 .176 .117 .031 .002 .000
11 .000 .000 .012 .071 .160 .160 .065 .007 .000
12 .000 .000 .004 .035 .120 .180 .114 .022 .000
13 .000 .000 .001 .015 .074 .166 .164 .055 .002
14 .000 .000 .000 .005 .037 .124 .192 .109 .009
15 .000 .000 .000 .001 .015 .075 .179 .175 .032
16 .000 .000 .000 .000 .005 .035 .130 .218 .090
17 .000 .000 .000 .000 .001 .012 .072 .205 .190
18 .000 .000 .000 .000 .000 .003 .028 .137 .285
19 .000 .000 .000 .000 .000 .000 .007 .058 .270
20 .000 .000 .000 .000 .000 .000 .001 .012 .122

5.18 Problems

5.18 On Monday mornings, the First National Bank only has one teller window open for deposits and withdrawals. Experience has shown that the average number of arriving customers in a 4- minute interval on Monday mornings is 2.8, and each teller can serve more than that number efficiently. These random arrivals at this bank on Monday mornings are Poisson distributed.

a. What is the probability that on a Monday morning exactly six customers will arrive in a 4- minute interval?

d. What is the probability that exactly three people will arrive at the bank during a 2- minute period on Monday mornings to make a deposit or a withdrawal? What is the probability that five or more customers will arrive during an 8- minute period?

See the attached file.

#### Solution Summary

The solution provides step by step method for the calculation of binomial and Poisson probabilities. Formula for the calculation and Interpretations of the results are also included.

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