# How do they get a probability of 71.57%

August 30, 2017

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
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
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
STUDENT TIP
Here is a chance to review
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.

Julie Ann Williams would like to find the probability that her project will be finished on or before the
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
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
STUDENT TIP
Here is a chance to review