Question: Machine. Being able to predict machine failures before they happen can save millions of dollars for manufacturing companies. Manufacturers want to be able to perform

Machine. Being able to predict machine failures before they happen can save millions of dollars for manufacturing companies. Manufacturers want to be able to perform preventive maintenance or repairs in advance to minimize machine downtime and often install electronic sensors to monitor the machines and their surrounding environment. A manager of a firm wants to explore the effect of percentage humidity (Low, Medium, or High) on machine failure (Yes or No). The accompanying table shows a portion of the data.

Machine Humidity Failure 1 Medium No 2 Medium No

⋮ ⋮ ⋮

480 High Yes

a. Use the data to construct a contingency table.

b. Find the probability that a randomly selected machine fails.

c. Find the probability that a randomly selected machine operates in high humidity.

d. Find the probability that a machine fails, given high humidity. Find the corresponding probabilities given low and medium humidity.

e. Is machine failure related to humidity? Explain using probabilities.

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