Chapter 04/4S Reliability Assignment 6 An office manager has received a report f

Question

Chapter 04/4S Reliability Assignment 6 An office manager has received a report from a consultant that includes a section on equipment replacement. The report indicates that scanners have a service life that is normally distributed with a mean of 41 months and a standard deviation of 4 months On the basis of this information, determine the proportion of scanners that can be expected to fail in the following time periods: Use Table A and Table B. 125 a. Before 38 months of service. (Round your intermediate calculations to 2 decimal places and final answers to 4 decimal places) Hint Proportion of scanners $38 b. Between 40 and 45 months of service. (Round your intermediate calculations to 2 decimal places and final answers to 4 decimal places.) Proportion of scanners 40

Explanation / Answer

Solution(a)
Given in the question
Mean = 41
Standard deviation = 4
P(Xbar<38) =?
Z=(38-41)/4 = -3/4 = -0.75
From the z table we found p-value = 0.2266
SO there is 22.66% proportion of scanners.
Solution(b):
P(40<Xbar<45) = P(Xbar<45) - P(Xbar<40)
Z = (45-41)/4 = 4/4 = 1
Z = (40-41)/4 = -1/4 = -0.25
P(40<Xbar<45) = 0.8413 - 0.4013 = 0.44
so there is 44% of scanners have service life time between 40 and 45
Solution(c)
P(39<Xbar<43) = P(Xbar<43)-P(Xbar<39)
Z = (43-41)/4 = 2/4 = 0.5
Z = (39-41)/4 = -2/4 = -0.5
P(39<Xbar<43) = 0.6915-0.3085 = 0.383

So there is 38.3% of scanners who have service life time is between +/- 2 months of mean time.

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