Question

It is well documented that a typical washing machine can last anywhere between 5 to 20 years. Let the life of a washing machine be represented by a lognormal variable, Y = eX where X is normally distributed. In addition, let the mean and standard deviation of the life of a washing machine be 9 and half years and 7 years, respectively. [You may find it useful to reference the z table.]

a. Compute the mean and the standard deviation of X. (Round your intermediate calculations to at least 4 decimal places and final answers to 4 decimal places.)

b. What proportion of the washing machines will last for more than 11 years? (Round your intermediate calculations to at least 4 decimal places, “z” value to 2 decimal places, and final answer to 4 decimal places.)

c. What proportion of the washing machines will last for less than 4 years? (Round your intermediate calculations to at least 4 decimal places, “z” value to 2 decimal places, and final answer to 4 decimal places.)

d. Compute the 90th percentile of the life of the washing machines. (Round your intermediate calculations to at least 4 decimal places, “z” value to 3 decimal places, and final answer to the nearest whole number.)

Answer 1

G iven Y- eX means a) LA 2 9.5 2

ven 2.39-18一2.03u 0.6549 86) t-3263-2-034y 0 6578 O , ( 635

0.9 0.65구8 0 6s 78 1 29 2 0 6S78 (y)9.8196 2-8 77 6 9
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