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Concept explainers
Times for a surgical procedure are
a.
![Check Mark](/static/check-mark.png)
Find the better procedure if the procedure must be completed within 28 minutes.
Answer to Problem 94CE
The better method for John to reach at the airport in 28 minutes to pick up his spouse is method A.
Explanation of Solution
Calculation:
It is given that the time on method A follows normal distribution with mean of 28 minutes, standard deviation of 4 minutes and the time on method B follows normal distribution with mean of 32 minutes, standard deviation of 2 minutes.
Normal distribution:
A continuous random variable X is said to follow normal distribution if the probability density function of X is,
Assume that the random variable X denotes the times for a surgical procedure.
For method A:
It is given that
Now, the probability to complete the procedure within 28 minutes using method A, implies that
Probability value:
Software procedure:
Step-by-step software procedure to obtain probability value using EXCEL is as follows:
- Open an EXCEL file.
- In cell A1, enter the formula “=NORM.DIST(28,28,4,1)”.
- Output using EXCEL software is given below:
Therefore,
Thus, the probability to complete the procedure within 28 minutes using method A is 0.5.
For method B:
It is given that
Now, the probability to complete the procedure within 28 minutes using method B, implies that
Probability value:
Software procedure:
Step-by-step software procedure to obtain probability value using EXCEL is as follows:
- Open an EXCEL file.
- In cell A1, enter the formula “=NORM.DIST(28,32,2,1)”.
- Output using EXCEL software is given below:
Therefore,
Thus, the probability to complete the procedure within 28 minutes using method B is 0.0228.
Therefore, there is to complete the procedure within 28 minutes using method A than by method B.
Thus, the better procedure if the procedure must be completed within 28 minutes is method A.
b.
![Check Mark](/static/check-mark.png)
Find the better procedure if the procedure must be completed within 38 minutes.
Answer to Problem 94CE
The better method for John to reach at the airport in 38 minutes to pick up his spouse is method B.
Explanation of Solution
Calculation:
For method A:
It is given that
Now, the probability to complete the procedure within 38 minutes using method A, implies that
Probability value:
Software procedure:
Step-by-step software procedure to obtain probability value using EXCEL is as follows:
- Open an EXCEL file.
- In cell A1, enter the formula “=NORM.DIST(38,28,4,1)”.
- Output using EXCEL software is given below:
Therefore,
Thus, the probability to complete the procedure within 38 minutes using method A is 0.9938.
For method B:
It is given that
Now, the probability to complete the procedure within 38 minutes using method B, implies that
Probability value:
Software procedure:
Step-by-step software procedure to obtain probability value using EXCEL is as follows:
- Open an EXCEL file.
- In cell A1, enter the formula “=NORM.DIST(38,32,2,1)”.
- Output using EXCEL software is given below:
Therefore,
Thus, the probability to complete the procedure within 38 minutes using method B is 0.9987.
Therefore, there is to complete the procedure within 38 minutes using method B than by method A.
Thus, the better procedure if the procedure must be completed within 38 minutes is method B.
c.
![Check Mark](/static/check-mark.png)
Find the better procedure if the procedure must be completed within 36 minutes.
Answer to Problem 94CE
The better procedure if the procedure must be completed within 36 minutes is method B.
Explanation of Solution
Calculation:
Coefficient of variation:
Coefficient of variation for a random variable X is defined as,
It is better to use a random variable with lower CV.
For method A:
It is given that
Now, the probability to complete the procedure within 36 minutes using method A, implies that
Probability value:
Software procedure:
Step-by-step software procedure to obtain probability value using EXCEL is as follows:
- Open an EXCEL file.
- In cell A1, enter the formula “=NORM.DIST(36,28,4,1)”.
- Output using EXCEL software is given below:
Therefore,
Thus, the probability to complete the procedure within 36 minutes using method A is 0.9772.
The CV for method A is,
For method B:
It is given that
Now, the probability to complete the procedure within 36 minutes using method B, implies that
Probability value:
Software procedure:
Step-by-step software procedure to obtain probability value using EXCEL is as follows:
- Open an EXCEL file.
- In cell A1, enter the formula “=NORM.DIST(36,32,2,1)”.
- Output using EXCEL software is given below:
Therefore,
Thus, the probability to complete the procedure within 36 minutes using method B is 0.9772.
The CV for method B is,
Therefore, there is same chance to complete the procedure within 36 minutes by method A and method B.
Now, the coefficient of variation for method B is less than method A.
Thus, the better procedure if the procedure must be completed within 36 minutes is method B.
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Chapter 7 Solutions
Applied Statistics in Business and Economics
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