# Four Poisson Distribution Problems

See attached file for clarity.

#3. Assume that the number of uninspected cars caught at a state police checkpoint is Poisson distributed with average 2.1 per hour. (a) What is the average number of cars caught in t hours? (b) What are P(no cars caught

in 14 hours? (c) P(at least 3 in 1.5 hours); (d) P(at least 1 car caught within 10 minutes of setting up the checkpoint)?

#7 a. Assume that batteries last for a time that is exponentially distributed with average 2 Months. If a transmitter needs one battery at a time and 4 (including the original) are taken on a expedition, what are (a)

P(Transmitter last at least 11 Months)?

#9. Louise sells encyclopedias door to door. She stops for the day after 4 sales. Assume that the time between sales is exponentially distributed. (a) If she can expect to work for 7 hours to make the 4 sales, what is the

parameter / ? What is the probability that she will stop (b) before 6 hours; (c) after 9 hours?

#10. Suppose that customers enter a store according to a Poisson stream with average 40.7 for a whole day. Suppose that 2 out of5 customers result in a sale. What is the distribution for the number of sales in half a day.

#### Solution Preview

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#3. Given the number of cars caught is a Poisson process at an average rate 2.1 per hour. Then if X denotes the number of cars caught in an interval of duration t hours, X follows Poisson distribution with parameter (i.e., mean )

a) Average number of cars caught in t hours is =

b) Number of cars caught in ¼ hours follows Poisson distribution with mean

2.1 * 0.25(= 0.525).

Probability that no cars caught in ¼ hours = = 0.5916

Note: can be obtained by using the MS excel function POISSON (0, 0.525, 0)

c) Number of cars caught in 1.5 hours follows Poisson distribution with mean

2.1*1.5 = 3.15.

Probability that at least 3 cars caught within 1.5 hours

= = 1-0.3904 = 0.6096

Note: can be obtained by using the MS excel ...

#### Solution Summary

The solution discusses four Poisson distribution problems.