In tossing of a five fair coin, find the chance of getting exactly 3 heads.

The mean of Binomials distribution is 20 and standard deviation is 4. Find the parameters of the distribution.

If x is a binomially distributed random variable with E(x) = 2 and van (x) = 4/3 Find P(x = 5)

The sum and product of the mean and variance of a binomial distribution are 24 and 128. Find the distribution.

Suppose A and B are two equally strong table tennis players. Which of the following two events is more probable:
(a) A beats B exactly in 3 games out of 4 or
(b) A beats B exactly in 5 games out of 8 ?

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

Assume the mean height of children to be 69.25 cm with a variance of 10.8 cm. How many children in a school of 1,200 would you expect to be over 74 cm tall?

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.

A sample of 125 dry battery cells tested to find the length of life produced the following resultd with mean 12 and SD 3 hours. Assuming that the data to be normal distributed , what percentage of battery cells are expected to have life
(i) more than 13 hours
(ii) less than 5 hours
(iii) between 9 and 14 hours

Weights of fish caught by a traveler are approximately normally distributed with a mean weight of 2.25 kg and a standard deviation of 0.25 kg. What percentage of fish weigh less than 2 kg?