Exercise 7.2: Poisson Distribution

Exercise 7.2

1. Define Poisson distribution.

2. Write any 2 examples for Poisson distribution.

3. Write the conditions for which the poisson distribution is a limiting case of binomial distribution.

4. Derive the mean and variance of poisson distribution.

5. Mention the properties of poisson distribution.

6. The mortality rate for a certain disease is 7 in 1000. What is the probability for just 2 deaths on account of this disease in a group of 400? Given e^(–2.8) = 0.06

7. It is given that 5% of the electric bulbs manufactured by a company are defective. Using poisson distribution find the probability that a sample of 120 bulbs will contain no defective bulb.

8. A car hiring firm has two cars. The demand for cars on each day is distributed as a Poisson variate, wjth mean 1.5. Calculate the proportion of days on which

(i) Neither car is used (ii) Some demand is refused

9. The average number of phone calls per minute into the switch board of a company between 10.00 am and 2.30 pm is 2.5. Find the probability that during one particular minute there will be (i) no phone at all (ii) exactly 3 calls (iii) atleast 5 calls

10. The distribution of the number of road accidents per day in a city is poisson with mean 4. Find the number of days out of 100 days when there will be (i) no accident (ii) atleast 2 accidents and (iii) at most 3 accidents.

11. Assuming that a fatal accident in a factory during the year is 1/1200, calculate the probability that in a factory employing 300 workers there will be atleast two fatal accidents in a year. (given e^–0.25 = 0.7788)

12. The average number of customers, who appear in a counter of a certain bank per minute is two. Find the probability that during a given minute (i) No customer appears (ii) three or more customers appear .

Answers:

6. 0.2352 

7. 0.0025 

8. (i) 0.2231 (ii) 0.1912 

9.(i) 0.08208 (ii) 0.2138 (iii) 0.1089 

10. (i) 2 days (ii) 91 days (iiii) 80 days 

11. 0.0265 

12. (i) 0.1353 (ii) 0.3235