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.

1. What is the probability that the average amount by which Massachusetts PayPal customershave exceeded their credit limit for a given month is less than 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?

P( $1380 $1420) =

Assume the PayPal analyst from problem #1 decides to expand his analysis and randomly selects 400 PayPal customers in Canada.Of these, he finds that exactly 80 had exceeded their credit limit for that month.

(a)What is the 95% confidence interval for the proportion of PayPal customers in Canada who had exceeded their credit limit for that month? (12 points