SOLUTION: please help 1)In planning for hot water requirements, the manager of the Crowne plaza hotel finds that guest spend a mean of 11.4 minutes each day in the shower. Assume that the

Question 433052: please help
1)In planning for hot water requirements, the manager of the Crowne plaza hotel finds that guest spend a mean of 11.4 minutes each day in the shower. Assume that the shower times are normally distributed with a standard deviation of 2.6 minutes. a) find the percentage of guess who shower more than 12 mintues. b)The hotel has installed a system that can provide enough hot water provided that the mean shower time for 84 quest is less than 12 mintues. If the hotel currently has 84 guest, find the probability that there will not be enough hot water . Does the current system appear to be effective ?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
1)In planning for hot water requirements, the manager of the Crowne plaza hotel finds that guests spend a mean of 11.4 minutes each day in the shower.
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Assume that the shower times are normally distributed with a standard deviation of 2.6 minutes.
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a) find the percentage of guests who shower more than 12 mintues.
z(12) = (12-11.4)/2.6 = 0.2308
P(x> 12)= P(z> 0.2308) = 0.4087
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b)The hotel has installed a system that can provide enough hot water provided that the mean shower time for 84 quest is less than 12 minutes. If the hotel currently has 84 guests, find the probability that there will not be enough hot water . Does the current system appear to be effective ?
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P(z< 12) = 1-0.4097 = 0.5913
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Cheers,
Stan H.
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