Exercise 3:

The lifetime of a roller bearing follows a lognormal distribution. The mean and standard

deviation of the corresponding normal distribution are 8 months and 2.5 months respectively.

b) Calculate the probability that a bearing will last more than 1 year.

OK I tried the following two ways, which one is correct:

A) P(X > 12) = 1 - P(X < 12) = 1 - P(e^w < 12)

= 1 - P(w < ln(12))

= 1 - P(Z<((ln(12)-8)/2.5)

= 1 - P(Z< -2.21)

= 1 - 0.014

= 0.986

B) F(X) = 1 - exp [ -(x/δ)^β ]

P(X > 12) = 1 - F(8)

= exp[-(12/8)^2.5]

= e^-2.756

= 0.064