The average rate of job submissions in a busy computer center is 5 per minute. I

Question

The average rate of job submissions in a busy computer center is 5 per minute. If it can be assumed that the number of submissions per minute interval is Poisson distributed, calculate the probability that: (a) What is the probability that three jobs will arrive in one minute? (b) What is the probability that three jobs will arrive in 30 seconds? (c) What is the mean and variance of this Poisson distribution? (d) At least 30 seconds will elapse between any two jobs. We have to accept or reject a large shipment of items. For quality control purposes, we collect a sample of 200 items and find 24 defective items in it. (a) Construct a 96% confidence interval for the proportion of defective items in the whole shipment. (b) The manufacturer claims that at most one in 10 items in the shipment is defective. At the 4% level of significance, do we have sufficient evidence to disprove this claim?

Explanation / Answer

Question-7

Part-a Parameter lambda =5 per minute

P(X=3)=0.1404 using excel function =POISSON(3,5,FALSE)

Part-b- Parameter lambda =5 per minute = 2.5 per 30 seconds

P(X=3)=0.2138 using excel function =POISSON(3,2.5,FALSE)

Part-c

Mean=lambda=5 per minute

Variance=lambda=5 per minute

Part-d

Y follows exponential distribution with parameter=1/lambda=1/5 minute=12 seconds

So. P(Y>=30)=0 using excel =1-EXPONDIST(30,12,TRUE)

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