6. (30 points) A worker has to retrieve 100 items. The time needed to retrieve a

Question

6. (30 points) A worker has to retrieve 100 items. The time needed to retrieve a single item has a mean and a variance of 9 minutes2. Assume that the times to retrieve the 100 items are time in minutes needed to retrieve all of 2.7 minutes independent and identically distributed. (a) What is the average 100 items? (b) What is the standard deviation of the total time (including specifying the appropriate units) needed to retrieve all 100 items? (c) What is the probability that the worker needs more than 5 hours to retrieve all 100 items?

Explanation / Answer

a) average time to retrieve all 100 items =100*2.7=270

b) and std deviaiton of total time =(9*100)1/2 =30

c) probability that need more than 5 hours(300 minutes) =P(X>300)=1-P(X<300)=1-P(Z<(300-270)/30)=1-P(Z<1)

=1-0.8413 =0.1587

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