Based on extensive testing, a manufacturer of washing machines believes that the distribution of the time Y (in years) until a major repair is required has a Weibull distribution with α = 2 and β = 4.
a. If the manufacturer guarantees all machines against a major repair for 2 years, what proportion of all new washers will have to be repaired under the guarantee?
b. Find the mean and standard deviation of the length of time until a major repair is required.
c. Find P (μ - 2σ ≤ Y ≤ μ + 2σ).
d. Is it likely that Y will exceed 6 years?