SOLUTION: 4. A nursing station in a large hospital has determined that the average amount of time applied to each patient on their floor has been about 36 minutes a day with a standard devia

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Question 518993: 4. A nursing station in a large hospital has determined that the average amount of time applied to each patient on their floor has been about 36 minutes a day with a standard deviation of 12 minutes.
a. What is the probability that a random sample of 49 patients would average less than 33 minutes of attention or care?
b. This nursing station knows that whenever the average time of care exceeds 42 minutes, they need to add another nurse. What is the likelihood of this?
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
A nursing station in a large hospital has determined that the average amount of time applied to each patient on their floor has been about 36 minutes a day with a standard deviation of 12 minutes.
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a. What is the probability that a random sample of 49 patients would average less than 33 minutes of attention or care?
z(33) = (33-36)/[12/sqrt(49)] = =1.75
P(x-bar < 33) = P(z < -1.75) = 0.0401
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b. This nursing station knows that whenever the average time of care exceeds 42 minutes, they need to add another nurse. What is the likelihood of this?
z(42) = (42-36)/12 = 1/2
P(x > 42) = P(z > 1/2) = 0.3085
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Cheers,
Stan H.