The life-time in hours of a certain electrical equipment has the normal distribution with mean=80 and standard deviation=16. (2.5+2.5=5 marks) I. What is the probability that the equipment that the equipment lasts at least 100 hours?

II. If the equipment has already lasted 88 hours, what is the conditional probability that it will last at least another 12 hours?

Q2. Five per cent of the blades produced by a blade manufacturing factory turn out to be defective. The blades are supplied in packets of 10. Use Poisson distribution to calculate the approximate number of packets containing no defective, one defective and two defective blades in a consignment of 100000 packets. (5 marks)

Q.3: In a locality, out of 5000 people residing, 1200 persons are above 30 years of age and 3000 persons are females. Out of the 1200 that are above 30, 200 are females. Suppose, after a person is chosen, you are told that the person is female. What is the probability that she is above 30 years of age? (5 marks)

Q4. A machine produces on average 20% defective bolts. A batch is accepted if a sample of 5 bolts taken from that batch contains no defective and rejected if the sample contains 3 or more defectives. In order case, a second sample is taken. What is the probability that the second sample is taken? What assumption is required for your answer? (5 marks)

Q5. In a distribution exactly normal, 31% of the items are under 45 and 8% are over 64. What is the mean and standard deviation of the distribution? (5 marks)