6.74 In automobiles, rubber boot seals are used to protect velocity joints and steering mechanisms.

Lifetimes of these boot seals depend on how much they come in contact with the metal shaft.

The lognormal distribution has been used to describe the lifetime of boot seals (Guerin and Hambli, J. Mechanical Designs, 2007).

a Using and months, determine the percent of boots expected to fail within 5 months.

b Determine the mean and variance of this distribution.

c The manufacturer of these rubber boots is interested in replacing free-of-charge at most 2% of its product under warranty. How long of a warranty should the manufacturer offer?