(7) A bank's loan officer rates applicants for credit. The ratings are normally distributed with a mean of 200 and a sandard deviation of 50. If 40 different applicants are randomly selected, find the probability that their mean is above 215. (7) (8) In planning for hot water requirements, the manager of the Luxurion Hotel finds that guests spend a mean of 11.4 min each day in the shower. Assume that the shower times \textit{z} are normally distributed with a standard deviation of 2.6 min. (a) Find the percentage of guests who shower more than 12 min. (i.e. the probability for a randomly selected guest to shower more than 12 min.) (8a) (b) The hotel has installed a system that can provide enough hot water provided that the mean shower time for 84 guests is less than 12 min. If the hotel currently has 84 guests, find the probability that there will not be enough hot water. (8b)
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Given: x = 12 minutes Ī¼ = 7 minutes Ļ = 2.6 minutes Substituting the values into the formula: z = (12 - 7) / 2.6 Show moreā¦
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