Test equipment in an automotive company dealership needs cal

Test equipment in an automotive company dealership needs calibration if 4.5% of service tests result in no maintenance required by a mechanic, and it is performing satisfactorily if 0.8% of service tests result in no maintenance required. Based on fifty service tests selected at random if the sample proportion of no maintenance required is greater than 0.02, the test equipment will be calibrated. Otherwise it will be allowed to continue operating. (a) What is the probability that the test equipment will be calibrated even though it is performing satisfactory? (b) What is the probability that the test equipment in need of calibration will be left in operation?

Solution

n =50

p for no maintenance = 4.5% = 0.045

X - no for no maintenance is binomial with p = 0.045 and n =50

If x> 0.02(50) = 1 then it is calibrated

P(X>1) = 0.6643

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b) P(X<=1) = 1-0.6643

=0.3357