Discuss the below:
State the Central Limit Theorem
The time spent by a factory worker A packing a box is a random variable with mean 3.5 minutes and standard deviation 1 minute. The times spent packing any two boxes are independent.
(i) What is the approximate probability that he packs 100 boxes in less than 6 hours?
(ii) What is the approximate probability that in 5.5 hours he will pack at least 90 and less than 100 boxes?
(iii) How long will he need to work for there to be 95% probability of packing 100 boxes?
(iv) A second worker B, does a similar job and the time it takes him to pack a box is a random variable with mean 3 minutes and standard deviation 1.2 minutes, independent of the time taken by A. The times spent by B packing any two boxes are independent. The two workers are assigned the job of packing 130 boxes each. Find the approximate probability that worker B will finish at least 50 minutes before worker A.