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 Medium No . .. NH Medium No 480 High Yes pictureClick here for the Excel Data File a. Use the data to construct a contingency table. Humidity Failure Low (L) Medium (M) High (H) Total No (N) Yes ()) 0 Total 0 0 0 0b. Find the probability that a randomly selected machine fails. (Round your answer to 4 decimal places.) P(Y) c. Find the probability that a randomly selected machine operates in high humidity. (Round your answer to 4 decimal places.) P(H) d. Find the probability that a machine fails, given high humidity. Find the corresponding probabilities given low and medium humidity. (Round your answers to 4 decimal places.) P(Y IH)d. Find the probability that a machine fails, given high humidity. Find the corresponding probabilities given low and medium humidity. (Round your answers to 4 decimal places.) P(Y | H) P ( YIL ) P(Y | M) e. Is machine failure related to humidity? Yes, because P( Y | L) = P( YI M) = P( Y | H) = P(Y) O No, because P( Y | L) # P( Y | M) = P( Y | H) = P(Y)