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**malaynsamani** XYZ Manufacturing 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:

Number of

Breakdowns------------- Probability

0------------------------------- 0.3

1 -------------------------------0.4

2------------------------------- 0.1

3------------------------------- 0.2

More than 3----------------- 0.0

(a) What is the expected number of breakdowns in any given day?

(b) What is the variance for this distribution?

(c) What is the probability that there will be at least 2 breakdowns in a day?

Answers:

a) probability of 1 breakdown + probability of 2 breakdowns + probability of 3 breakdowns = 0.4+0.1+0.2 = 0.7 (70%)

c) Atleast two break downs means 2 and above. ie. probability of 2 breakdowns + probability = 0.1+0.2 = 0.3 (30%)