1-7 Susan Williams has been the production manager of Medical Supplies, Inc. for
ID: 444469 • Letter: 1
Question
1-7 Susan Williams has been the production manager of Medical Supplies, Inc. for the past 17 years. Medical Supplies Inc. is a producer of bandages and arm slings. During the past 5 y ears, the demand for No-Stick bandages has been fairly constant. On the average, sales have been about 87,000 packages of No-Stick. Susan has reason to believe that the distribution of No-Stick follows a normal curve, with a standard deviation of 4,500 packages.
What is the probability that sales will be less than 80,000 packages?
1-8 The time to complete a construction project is normally distributed with a mean of 45 weeks and standard deviation of 4.5 weeks.
a.What is probability the project will be finished in 53 weeks or less?
b.What is the probability the project will be finished in 40 weeks or less?
c.What is probability the project will take more than 57 weeks?
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Explanation / Answer
1-7 Susan Williams has been the production manager of Medical Supplies, Inc. for the past 17 years. Medical Supplies Inc. is a producer of bandages and arm slings. During the past 5 y ears, the demand for No-Stick bandages has been fairly constant. On the average, sales have been about 87,000 packages of No-Stick. Susan has reason to believe that the distribution of No-Stick follows a normal curve, with a standard deviation of 4,500 packages.
What is the probability that sales will be less than 80,000 packages?
Let us represents number of No-stick bandages as X, therefore we can say that X follows normal distribution with mean 87,000 and standard deviation 4,500 and it is required to find Probability ( X < 80,000 )
For finding probability we need to make use of Standard Normal variable Z by using the formula Z = (X-mean)/S.D.
In other words, define Z= (X-87,000) / 4,500 where this Z follows standard normal distribution with mean zero and standard deviation 1. Hence Prob.( X < 80,000 ) = Prob. ( Z < (80000-87000)/4500) = Prob.(Z< (-1.56)) which is also same as Prob.(Z>1.56) ( Normal curve is symmetrical about its mean)
Using Standard normal distribution tables we get Prob.(Z<-1.56) = Prob.(X < 80,000) = .5 - .4406 = .0594
Therefore the probability that sales will be less than 80,000 packages may be approximately .06 (say 6% channces)
1-8 The time to complete a construction project is normally distributed with a mean of 45 weeks and standard deviation of 4.5 weeks.
a.What is probability the project will be finished in 53 weeks or less?
Prob.(X <= 53) = Prob.(Z <= (53-45)/4.5) = Prob. (Z <= 1.78) = .9625 (.5+.4625)
b.What is the probability the project will be finished in 40 weeks or less?
Prob.(X <= 40) = Prob.(Z <= (53-45)/4.5) = Prob. (Z <= -1.11) = .1335 (.5-.3665)
c.What is probability the project will take more than 57 weeks?
Prob. (X >= 57) = Prob.(Z >= (57-45)/4.5) = Prob.(Z>=2.67) = .0038 (.5-.4962)
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