Question 1: When a customer places an order with Office Works, a computerised Accounting Information System (AIS) automatically checks to see if the customer has exceeded his or her credit limit. Past records indicate that the probability of customers exceeding their credit limit is 0.07. Suppose that, on a given day, 20 customers place orders. Assume that the number of customers that the AIS detects as having exceeded their credit limit is distributed as a binomial random variable. What is the probability that 2 or more customers will exceed their limits on that given day?
Question 2: A statistical analysis of 1,000 long-distance telephone calls made from the headquarters of the Bricks and Clicks Computer Corporation indicates that the length of these calls is normally distributed, with µ = 240 seconds and σ = 40 seconds.
(i) What is the probability that a call lasted less than 190 seconds?
(ii) What is the probability that a call lasted between 200 and 300 seconds?
(iii) What is the length of a call if only 1% of all calls are shorter?