Historical records indicate that X is a normally distributed random variable with a mean of $1400 and a standard deviation of $120.

The analyst decides to engage in repeated sampling by conducting surveys in each of the 50 US states.Each sample will consist of 100 PayPal customers.

(a)What is the probability that the average amount by which Massachusetts PayPal customers have exceeded their credit limit for a given month is less than $1360?

P( $1360) =

(b)What is the probability that the average amount by which Massachusetts PayPal customers exceed their credit limit for a given month is between $1380 and $1420? (7 points)