The lifetime of disc brake pads varies according to a normal distribution with mean µ = 50,000 miles and standard deviation σ = 3000 miles. (a) What is the probability the lifetime of a random sampled...

The lifetime of disc brake pads varies according to a normal distribution with mean µ = 50,000 miles and standard deviation σ = 3000 miles. (a) What is the probability the lifetime of a random sampled brake pad is 47,000 miles or less? (b) What is the distribution of the mean lifetime X of 9 randomly sampled brake pads? (c) What is the probability the mean lifetime of 9 randomly sampled brake pads is less than 47,000 miles? (d) Could you estimate the probabilities from parts (a) and (c) if the lifetime of a brake pad has a skewed distribution?