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

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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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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