The lifetime X, (time until battery dies) of a battery of a hybrid car from Company T, is normally distributed with a mean ? = 47 months and a standard deviation ? = 8.2 months. Suppose that we take a random sample of 63 hybrid cars from company T and determine the lifetime of the battery, in months, for each car chosen. Let M be the sample mean of the 63 lifetime measurements. Let S be the sum of the 63 lifetime measurements.

a) What is the probability that X < 50?

b) What is the probability that X > 50?

c) What is the probability that all of the 63 measurements are greater than 33?

d) What is the expected value of S?

e) What is the standard deviation of S?

f) What is the probability that S-63*47 >10?

g) What is the standard deviation of S-63*47

h) What is the expected value of M?

i) What is the standard deviation of M? j) What is the probability that M >50? k) What is the standard deviation of 63*M? l) If the probability of X > k is equal to .6, then what is k?