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 2 minutes, while method B has a mean of 32 minutes and a standard deviation of 1.0 minutes. (a) Which procedure is preferred if the procedure must be completed within 30 minutes? multiple choice 1Method AMethod BEither Method (b) Which procedure is preferred if the procedure must be completed within 34.0 minutes? multiple choice 2Either MethodMethod AMethod B (c) Which procedure is preferred if the procedure must be completed within 31 minutes? multiple choice 3Method BEither MethodMethod A

Answered: Times for a surgical procedure are…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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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 2 minutes, while method B has a mean of 32 minutes and a standard deviation of 1.0 minutes.

(a) Which procedure is preferred if the procedure must be completed within 30 minutes?

multiple choice 1

Method A
Method B
Either Method

(b) Which procedure is preferred if the procedure must be completed within 34.0 minutes?

multiple choice 2

Either Method
Method A
Method B

(c) Which procedure is preferred if the procedure must be completed within 31 minutes?

multiple choice 3

Method B
Either Method
Method A

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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Given Information:

Times for a surgical procedure are normally distributed.

Method A has a mean of 28 minutes and a standard deviation of 2 minutes, while method B has a mean of 32 minutes and a standard deviation of 1.0 minutes.

Let X denote the time for a surgical procedure of Method A and X is normally distributed with mean $μ = 28$ and $σ = 2$ .

Let Y denote the time for a surgical procedure for Method B and Y is normally distributed with mean $μ = 32$ and $σ = 1.0$

(a) Which procedure is preferred if the procedure must be completed within 30 minutes:

Z-score is a measure which indicates how many standard deviations away, a data value is, from the mean. It is given by the formula:

$Z = \frac{X - μ}{σ}$

Z-score for method A is:

$Z = \frac{30 - 28}{2} = 1.00$

Using standard normal table, probability or area corresponding to the left of z-score (1.00) is 0.84134

Z-score for method B is:

$Z = \frac{30 - 32}{1.0} = - 2.00$

Using standard normal table, probability or area corresponding to the left of z-score (-2.00) is 0.02275

Since, $P (X \leq 30) = 0.84134$ is greater than $P (Y \leq 30) = 0.02275$ , Method A is preferred.

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