The life time of a heavy lift machine is normally distributed, with mean of 7.2 years and standard d

The life time of a heavy lift machine is normally distributed, with mean of 7.2 years and standard deviation of 2.3 years.

a.If the manufacturer guarantees the machine for 3 years, what is the chance that a randomly chosen machine will wear out before the guarantee has expired?

b.If the manufacturer is willing to replace only 2% of all machines due to early failure, how should he change the guarantee?

c.If we choose a sample of 20 machines, what is the chance that the average life time for the sample is less than 8 years?