1. (a) The life time of a certain brand of bulbs produced by a company is normally distributed, with mean 210 hours and standard deviation 56 hours. What is the probability that a bulb picked at random from this company’s products will have a life time of: (i) (ii) (iii)at least 300 hours,
at most 100 hours, between 150 and 250 hours.
(b) In a contest, two friends, Kofi and Mensah were asked to solve a problem. The probability that Kofi will solve it correctly is and the probability that Mensah
will solve it correctly is . Find the probability that neither of them solved it correctly.
2. Suppose that the random variable, X, is a number on the biased die and the p. d.f. of X is as shown below;
X
1
2
3
4
5
6

P(X=x)
1/6
1/6
1/5
k
1/5
1/6

a) Find;
(i) (ii) (iii) (iv) (v)the value of k. E(X)
E(X2) Var(X) P(1 £X <5)
b) If events A and B are such that they are independent, and P(A) = 0.3 with P(B) = 0.5;
i. ii. Find P(A n B) and P(AUB)
Are A and B mutually exclusive? Explain.
c) In how many ways can the letters of the word STATISTICS be arranged?