Question: In a given large town the number of children, X, in a family chosen at random has the following distribution:

x   P(X=x)

0   0.2

1   0.4

2   0.25

3   0.1

4   0.05

a) Find the mean and variance of X.

b) State the approximate distribution for the total number of children in 150 families.

On what theoretical basis can this approximation be made (state the reason)?

c) If a sample of 150 families is chosen at random what are the approximate probabilities there will be

i. more than 250 children present

ii. between 220 and 250 children present.

d) When catering for the children of these 150 families the organisers of a picnic for them wish to be 95% certain that they have provided enough food for the children.

How many children should they cater for?