Question

1. Assume that there is a 0.05 probability that a sports playoff series will last four games, a 0.35 probability that it will last five games, a 0.45 probability that it will last six games, and a 0.15 probability that it will last seven games.

Let the random variable x be the number of games in a series. Find the smallest usual value for this probability distribution; round your answer to two decimal places.

2. A machine has 15 identical components which function independently. The probability that a component will fail is 7.2%. The machine will stop working if more than 3 components fail. Find the probability that the machine will not stop working.

Answer 1

1:

First we need find the mean and SD of the probability distribution. Following table shows the calculations:

X	P(X=x)	xP(X=x)	x^2*P(X=x)
4	0.05	0.2	0.8
5	0.35	1.75	8.75
6	0.45	2.7	16.2
7	0.15	1.05	7.35
Total	1	5.7	33.1

μ = E(X) xPlX = z) = 5.7

PP(X =x) rP(X = 2) | = 0.7810

The smallest usual value is

μー20-5.7-2 . 0.78 10 4.138

Answer: 4.14

2:

The probability that the machine will not stop working is

3) = Σ ( T)) (0.072)"(1-0.072)15-1-0.9807 P(X