The Readylite Company produces a flashlight in which product managers are trying

Question

The Readylite Company produces a flashlight in which product managers are trying to decide how long a warranty to issue. If the managers believe the life of the flashlight follows a normal distribution with a mean of one and one-half years and a standard deviation of one-half years:

a) What percentage of flashlights sold can they anticipate will be returned within the first years?

b) What percentage of flashlights sold can they anticipate will be returned within the first two and one-half years?

Explanation / Answer

Given are the following data :

Mean life of flashlight = m = 1.5 years

Standard deviation of life of flashlight = Sd = 1.5 years

Let corresponding Z value for probability that the flashlight will turn out to be out of order and returned within first year = Z1

Therefore,

M + Z1 x Sd = 1

Or, 1.5 + 1.5Z1 = 1

Or 1.5.Z1 = - 0.5

Or, Z1 = - 0.5/1.5 = - 0.33 ( rounded to 2 decimal places)

Thus, Probability for Z = - 0.33 as derived from standard normal distribution table 0.37070

Thus percentage of flashlight sold which is anticipated to be returned within first year

= 0.37070 x 100 = 37.07 %

PERCENTAGE OF FLASHLIGHT SOLD ANTICIPATED TO BE RETURNED WITHIN 1ST YEAR = 37.07%

Let corresponding Z value for probability that the flashlight will turn out to be out of order and returned within first year = Z2

Therefore,

M + Z2 x Sd = 1

Or, 1.5 + 1.5Z1 = 2.5

Or 1.5.Z1 = 1

Or, Z1 = 1/1.5 = 0.67 ( rounded to 2 decimal places )

Thus, Probability for Z = 0.67 as derived from standard normal distribution table 0.74857

Thus percentage of flashlight sold which is anticipated to be returned within first year

= 0.74857 x 100 = 74.86 % ( rounded to 2 decimal places )

PERCENTAGE OF FLASHLIGHT SOLD ANTICIPATED TO BE RETURNED WITHIN FIRST TWO AND HALF YEARS = 74.86 %

PERCENTAGE OF FLASHLIGHT SOLD ANTICIPATED TO BE RETURNED WITHIN 1ST YEAR = 37.07%

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