A Bank of 10 Machines Requires Regular Periodic Service

question 64

Multiple Choice

A bank of 10 machines requires regular periodic service. Machine running time and service time are both exponential. Machines run for an average of 44 minutes between service requirements, and service time averages six minutes per machine. What is the average number of machines down when there is one operator?

• A)1.49
• B)3.35
• C)4.40
• D)6.65
• E)8.51

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Definitions:

Covariance

A measure that indicates the extent to which two variables change together, but does not indicate the strength of their relationship.

Independent

Not influenced by or dependent on another variable; in statistics, it often means that the occurrence of one event does not affect the probability of another event.

COV(X,Y)

Covariance between two variables X and Y, measuring the extent to which the variables change together and indicating the direction of their linear relationship.

Marginal Probability

The probability of occurring of a single event without consideration of any other events; it’s the likelihood of a single outcome.