Purchase Solution

Four Poisson Distribution Problems

Not what you're looking for?

Ask Custom Question

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.

Purchase this Solution

Solution Summary

The solution discusses four Poisson distribution problems.

Solution Preview

See the attached file for full solution.

#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 ...

Purchase this Solution


Free BrainMass Quizzes
Know Your Statistical Concepts

Each question is a choice-summary multiple choice question that presents you with a statistical concept and then 4 numbered statements. You must decide which (if any) of the numbered statements is/are true as they relate to the statistical concept.

Terms and Definitions for Statistics

This quiz covers basic terms and definitions of statistics.

Measures of Central Tendency

This quiz evaluates the students understanding of the measures of central tendency seen in statistics. This quiz is specifically designed to incorporate the measures of central tendency as they relate to psychological research.

Measures of Central Tendency

Tests knowledge of the three main measures of central tendency, including some simple calculation questions.