On-the-job injuries in a textile mill severe enough to lead a worker to ask for

Question

On-the-job injuries in a textile mill severe enough to lead a worker to ask for disability leave occur at the rate of 0.1 per day. We model using the Poisson distribution. 1. a. b. c. d. What 2 assumptions do we make? What may make these assumptions unrealistic for our situation? What is the probability that two injuries will occur during the next (six-day) workweek? The probability that four injuries will occur over the next two workweeks is not the square of your answer to part (a). Explain why not and find it.

Explanation / Answer

Question 1

(a) THere are 2 assumptions we make here.

(i) Independence: Events must be independent. Like taking leave on a perticular day shall be independent from taking leave next day.

(ii) Homogeneity: The rate at which leaves are taken shall be homogeneous.

(b) When there are large number of cinsecutive holidays will be taken due to anyreason. That will make these assumptions invalid.

(c) Two injuries in next 6 day work week.

Expectd number of injuries in next 6 days = 6 * 0.1 = 0.6 leave

Pr(X = 2) = POISSON ( X =0.6; 2) = e-0.6 (0.6)2 /2! = 0.0988

(d) Now we have to find the number of injuries in next two work weeks or say 12 days shall be 4 .

Expectd number of injuries in next 2 days = 12 * 0.1 =1.2 leave

Pr(X = 4) = POISSON ( X = 4; 1.2) = e-1.2 (1.2)4 /4 = 0.0260

this value is not sqqaure of the probability of c part. It is because the two weeks are not independent in nature. Taking 2 leaves in first week and taking 4 leaves in 2 weeks are not 2 events that are independent.

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