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 = e^X where X is normally distributed. In addition, let the mean and standard deviation of the life of a washing machine be 11 and half years and 2 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.)

Mean:
Standard Deviation:

b. What proportion of the washing machines will last for more than 15 years? (Round your intermediate calculations to at least 4 decimal places, “z” value to 2 decimal places, and final answer to 4 decimal places.)

Proportion:

c. What proportion of the washing machines will last for less than 8 years? (Round your intermediate calculations to at least 4 decimal places, “z” value to 2 decimal places, and final answer to 4 decimal places.)

Proportion:

d. Compute the 80th 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.)

80th percentile:

Answer 1