1 Statistics and Probabilty 1 The probability a copy machine

#1 Statistics and Probabilty

1. The probability a copy machine breaks in any given week is .4. a) Compute the probability it is broken exactly 3 out of 8 weeks b) If it costs $ 50 to repair, how much would you expect to spend on repairs over an 8 month period?

Solution

1) Prob that a copy machine breaks in any week =0.4

Let X - no of weeks it breaks

X is binomial with (8,0.4)

Reqd prob = P(X=3)

= 8C3(0.4)³(0.6)⁷

= 56(0.064)(0.028)

= 0.1003

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b) Repair cost = 50

Expected repairs in 8 weeks = binomial mean = np

= 8(0.4) = 3.2

Repair cost for 3.2 = 3.2(50)

= 150+10 = 160