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^XwhereXis normally distributed. In addition, let the mean and standard deviation of the life of a washing machine be 5 years and 4 years, respectively.[You may find it useful to reference thez table.]

a.Compute the mean and the standard deviation ofX.(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 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.)

c.What proportion of the washing machines will last for less than 3 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 75th 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.)