It is well documented that a typical washing machine can last anywhere between 5 to 12 years. Let the life of a washing machine be represented by a log normal variable, Y = eX, where X is normally distributed. In addition, let the mean and standard deviation of the life of a washing machine be 8 years and 4 years, respectively. 

a. Compute the mean and the standard deviation of X.

b. What proportion of the washing machines will last for more than 10 years?

c. What proportion of the washing machines will last for less than 6 years?

d. Compute the 90th percentile of the life of the washing machines.