#1:(14 points)

"PayPal is an international e-commerce business allowing payments and money transfers to be made through the Internet. Online money transfers serve as electronic alternatives to paying with traditional paper methods, such as checks and money orders." (Wikipedia)Many individuals set up PayPal accounts with a credit card such as Visa or MasterCard; however, sometimes these cards get 'maxed out' and the institution which issued the card (e.g., a bank) informs PayPal that the individual has exceeded their credit limit.

An analyst at PayPal has defined a random variable:

LetX =amount by which the individual customer has exceed their credit limit

for a given month (measured in US dollars)

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

Executives at PayPal are considering different strategies for dealing with customers that exceed their credit limit, and have asked the analyst to collect more data before they make any policy changes.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?(7 points)

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)

P( $1380 $1420) =

QUESTION 1a.

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

95% Confidence Interval =

(B)In one sentence, explain the two numeric values you found in part (a). (4 points)