Question

C1: Snow Manufacturing Co. has 6 machines that perform a particular task. Breakdowns occur frequently for this machine. Past records indicate that the number of breakdowns that occur each day is described by the following probability distribution: SK2: 5 marks Number of Probability Breakdowns 0.2 0.3 0.4 More than 3 0.0 Required: 1. What is the expected number of breakdowns in any given day? (2 marks) 2. What is the variance for this distribution? (1 mark) 3. What is the probability that there will be at least 3 breakdowns in a day? (1 mark) 4. What is the probability that there will be at least 1 breakdowns in a day ? (Imark)

Answer 1

1) Expected number of Breakdowns in any given day, E(X) = 0*.1+1*.2+2*.3+3*.4

= 2

2) Variance, V(X) = .1*(0-2)^2+.2*(1-2)^2+.3*(2-2)^2+.4*(3-2)^2

= 1

3) Probability of at least 3 breakdowns in a day = Probability of 3 breakdowns + Probability of more than 3 breakdowns

= 0.4+0

= 0.4

4) Probability of at least 1 breakdowns in a day = 1 - Probability of 0 breakdown

= 1 - 0.1

= 0.9