Question 25

Our department seminar room is lit by 7 light bulbs, controlled by a single switch. A minimum of 3 lights are needed for the room to be usable. Suppose the lifetime of the brand of light bulbs fitted is exponentially distributed with a mean of 400 hours. Assume a seminar lasts exactly 1 hour, and that the lights are switched on only during the seminar. What is the probability that after 500 seminars, exactly 3 bulbs do not need to be replaced? You may need to use a calculator. 

Give your answer rounded to 4 decimal places.

Question 10 The weekly demand for a product approximately has a normal distribution with mean 1,000 and standard deviation 200. The current on hand inventory is 2,200 and no deliveries will be occurring in the next two weeks. Assuming that the demands in different weeks are independent,
a) What is the probability that the demand in each of the next 2 weeks is less than 1,100?
b) What is the probability that the total of the demands in the next 2 weeks exceeds 2,200?

4. In proof testing of circuit boards, the probability that any particular diode will fail is 0.01. Suppose a circuit board contains 300 diodes.
(a) How many diodes would you expect to fail on a circuit board, and what is the standard deviation of the number that are expected to fail?
(b) With Poisson distribution approximation, what is the (approximate) probability that at least one diode will fail on a randomly selected board? Round your answer to 2 decimal places.
(c) If ten boards are shipped to a particular customer, how likely is it that at least two of them will work properly? (A board works properly only if all its diodes work)