# How do they get a probability of 71.57%

I need to understand how they got the probability of 71.57%. To help you see the probability curve this problem can be located in the textbook: O P E R AT I O N S

MANAGEMENT

Sustainability and Supply Chain Management 11th edition: the problem is example 10 on page 77 or if you have the same page issues that we do it is located on page 117 but it is example 10.

Julie Ann Williams would like to find the probability that her project will be finished on or before the

16-week Earth Day deadline.

APPROACH c To do so, she needs to determine the appropriate area under the normal curve. This is

the area to the left of the 16th week.

SOLUTION c The standard normal equation can be applied as follows:

Z = (Due date – Expected date of completion)/sp (3-9)

= (16 weeks – 15 weeks)/1.76 weeks = 0.57

where Z is the number of standard deviations the due date or target date lies from the mean or expected

date.

Referring to the Normal Table in Appendix I, we find a Z value of 0.57 to the right of the mean indicates

a probability of 0.7157. Thus, there is a 71.57% chance that the pollution control equipment can be

put in place in 16 weeks or less. This is shown in Figure 3.13.

Example 10 PROBABILITY OF COMPLETING A PROJECT ON TIME

INSIGHT c The shaded area to the left of the 16th week (71.57%) represents the probability that the

project will be completed in less than 16 weeks.

LEARNING EXERCISE c What is the probability that the project will be completed on or before the

17th week? [Answer: About 87.2%.]

RELATED PROBLEMS c 3.14d, 3.17f, 3.21d, e, 3.22b, 3.24

15

Weeks

16

Weeks

0.57 Standard Deviations

Time

Probability

(T ? 16 Weeks)

is 71.57%

Figure 3.13

Probability That Milwaukee

Paper Will Meet the 16-Week

Deadline

STUDENT TIP

Here is a chance to review

your statistical skills and use

of a normal distribution table

(Appendix I).

H

ISBN 1-269-21506-X

Operations Management: Sustainability and Supply Chain Management, Eleventh Edition, by Jay Heizer and Barry Render. Published by Pearson.

Copyright

Julie Ann Williams would like to find the probability that her project will be finished on or before the

16-week Earth Day deadline.

APPROACH c To do so, she needs to determine the appropriate area under the normal curve. This is

the area to the left of the 16th week.

SOLUTION c The standard normal equation can be applied as follows:

Z = (Due date – Expected date of completion)>sp (3-9)

= (16 weeks – 15 weeks)>1.76 weeks = 0.57

where Z is the number of standard deviations the due date or target date lies from the mean or expected

date.

Referring to the Normal Table in Appendix I, we find a Z value of 0.57 to the right of the mean indicates

a probability of 0.7157. Thus, there is a 71.57% chance that the pollution control equipment can be

put in place in 16 weeks or less. This is shown in Figure 3.13.

Example 10 PROBABILITY OF COMPLETING A PROJECT ON TIME

INSIGHT c The shaded area to the left of the 16th week (71.57%) represents the probability that the

project will be completed in less than 16 weeks.

LEARNING EXERCISE c What is the probability that the project will be completed on or before the

17th week? [Answer: About 87.2%.]

RELATED PROBLEMS c 3.14d, 3.17f, 3.21d, e, 3.22b, 3.24

15

Weeks

16

Weeks

0.57 Standard Deviations

Time

Probability

(T ? 16 Weeks)

is 71.57%

Figure 3.13

Probability That Milwaukee

Paper Will Meet the 16-Week

Deadline

STUDENT TIP

Here is a chance to review

your statistical skills and use

of a normal distribution table

(Appendix I).

H

ISBN 1-269-21506-X

Operations Management: Sustainability and Supply Chain Management, Eleventh Edition, by Jay Heizer and Barry Render. Published by Pearson.

Copyright

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