Question

Exercise 6-73 Algo

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 = e^X where X is normally distributed. In addition, let the mean and standard deviation of the life of a washing machine be 8 and half years and 6 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 10 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 65th 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