Times for a surgical procedure are normally distributed. There are two methods. Method A has a mean of 28 minutes and a standard deviation of 6 minutes, while method B has a mean of 32 minutes and a standard deviation of 4 minutes. (a) Which procedure is preferred if the procedure must be completed within 28 minutes? (b) Thirty-eight minutes? (c) Thirty-six minutes? Explain your reasoning fully.
Method A has a mean of 28 minutes and a standard deviation of 6 minutes, while
method B has a mean of 32 minutes and a standard deviation of 4 minutes. (a)
Which procedure is preferred if the procedure must be completed within 28
minutes? (b) Thirty-eight minutes? (c) Thirty-six minutes? Explain your reasoning
fully.
(a)
The mean time for method A is 28 minutes, and the standard deviation is 6 minutes. This means that 68% of the procedures will take between 22 minutes and 34 minutes. The remaining 32% of the procedures will take either less than 22 minutes or more than 34 minutes.
The mean time for method B is 32 minutes, and the standard deviation is 4 minutes. This means that 50% of the procedures will take between 28 minutes and 36 minutes. The remaining 50% of the procedures will take either less than 28 minutes or more than 36 minutes.
In this case, we want the procedure to take less than 28 minutes. The probability that method A will take less than 28 minutes is 68%, while the probability that method B will take less than 28 minutes is 50%. Therefore, method A is preferred.
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