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 two years and a standard deviation of six months:
a. What percentage of flashlights sold can they anticipate will be returned within the first two years?
b. What percentage of flashlights sold can they anticipate will be returned within the first three years?
c. What percentage of flashlights sold can they anticipate will be returned within the first two and one-half years?
Mean = 2 years stdev = 6 months = 0.5 years Z = (x - mu)/stdev
a) percentage of flashlights sold can they anticipate will be returned within the first two years is given by area under the Z curve on the left hand side of point x = 2 = P[Z = (2 - 2)/0.5] = P[Z = 0] = 0.50 = 50%
b) percentage of flashlights sold can they anticipate will be returned within the first three years is given by area under the Z curve on the left hand side of point x = 3 = P[Z = (3 - 2)/0.5] = P[Z = 2] = 0.9772 = 97.72%
a. P(X<2) = P((X-mean)/s <(2-2)/0.5) =P(Z<0) =0.5 (from standard normal table)
b. P(X<3) = P(Z<(3-2)/0.5) =P(Z<2) =0.9772 (from standard normal table)
c) percentage of flashlights sold can they anticipate will be returned within the first two and one half years is given by area under the Z curve on the left hand side of point x = 2.5 = P[Z = (2.5 - 2)/0.5] = P[Z = 1] = 0.8413 = 84.13%
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