If the average rain falls on 9 days in every thirty days, find the probability that rain will fall on atleast two days of a given week.

An insurance company has discovered that only about 0.1 per cent of the population is involved in a certain type of accident each year. If its 10,000 policy holders were randomly selected from the population, what is the probability that not more than 5 of its clients are involved in such an accident next year? (e⁻¹⁰=.000045)

If the probability that an individual suffers a bad reaction from injection of a given serum is 0.001, determines the probability that out of 2,000 individuals
(a) exactly 3, and
(b) more than 2 individuals will suffer a bad reaction.

If X is a normal variate with mean 30 and SD 5. Find the probabilities that 
(i) 26 ≤ X ≤ 40
(ii) X > 45

The marks obtained in a certain exam follow normal distribution with mean 45 and SD 10. If 1,300 students appeared at the examination, calculate the number of students scoring
(i) less than 35 marks and
(ii) more than 65 marks.