Times between successive crashes of a computer system were generated for a 6-months period and are given in increasing order as follows (time in hours): 1, 10, 20, 30, 40, 52, 63, 70, 80, 90, 100, 102, 130, 140, 190, 210, 266, 310, 530,590, 640, 1340. The value of parameter α and Mean (1/α) is given as 0.00435 and 230 hrs, respectively. Use kolmogrov-Smirnov test to examine the goodness of fit of exponential distribution.

The telephone department will install a second booth when convinced that an arrival would expect waiting for at least 3 minutes for phone call. By how much should the flow of arrivals increases in order to justify a second booth?

Two cards are drawn one at a time from a 52-card standard deck. Then the probability that the second card is red, if the drawing is done with replacement is 1/2

A leather bag manufacturing company supplies bags in lots of size 200 to a buyer. A sample of 2 begs is drawn and the corresponding lot is accepted if and only if both begs are nondefective. The company and the buyer decide that AQL = 0.04 and LTDD = 0.10. If there are 15 defective bags in each lot, compute the

(i) Probability of accepting the lot,

(ii) Producer’s risk and consumer’s risk,

(iii) AOQ, if the rejected lots are screened and all defective bags are replaced by nondefectives, and

(iv) Average total inspection.

Roll two fair dice, one red and one blue, and consider the events:

A: “The red die lands on 4”,

B: “The sum on the dice is 9” and

C: “The blue die lands on an odd number”.

Determine which pairs of events are independent.

A solicitors’ firm employs typists on hourly price-rate basis for their daily work. There are five typists and their charges and speed are different. According to an earlier understanding only one job is given to one typist and the typist is paid for a full hour even if he works for a fraction of an hour. Find the least cost allocation for the following data:

The Set $ ={(x, y) : 0 ≤ y ≤ 5 when 0 ≤ x≤ 2 and 3≤ y≤ 5 when 2≤ x ≤ 7 } is not a convex set.