I. The Readylite Company produces a flashlight in which product managers are try
ID: 328212 • Letter: I
Question
I. The Readylite Company produces a flashlight in which product managers are trying to decide how long a warranty to ssue. If the managers believe the life of the flashlight follows a normal distribution with a mean of 3 years and a standard deviation of 1.5 years): a. What percentage of flashlights sold can they anticipate b. What percentage of flashlights sold can they anticipate c. What percentage of flashlights sold can they anticipate will be returned within the first year? will be returned within two years? will be returned between the first year and the third year? II. The guidance system of a ship has four modules that must all function properly for the system to work. Two of the modules have reliability of .96, the other two have a reliability of .95. a. Compute the reliability of the system. b. A backup system identical to the first will be added to the ship. The backup will be switched on automatically if the first system fails. Assuming that the switch to the backup works perfectly, what is the reliability of the ship's guidance system now? Show your calculations.Explanation / Answer
Q. I.
Mean, m = 3 years
Std deviation, s = 1.5 years
a) x = 1 year
z = (x-m)/s = (1-3)/1.5 = -1.33
Percentage of flashlights anticipated to be returned within the first year = NORMSDIST(-1.33) = 0.0912 or 9.12 %
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b) x = 2 years
z = (x-m)/s = (2-3)/1.5 = -0.667
Percentage of flashlights anticipated to be returned within the first two years = NORMSDIST(-0.667) = 0.2525 or 25.25 %
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c) For 3 years, x = 3 years
z = (x-m)/s = (3-3)/1.5 = 0
Percentage of flashlights anticipated to be returned within the first three years = NORMSDIST(0) = 0.5
Percentage of flashlights anticipated to be returned between the first and the third year = 0.5 - 0.0912 = 0.4088 or 40.88 %