A Subway restaurant in Scotsbluff, Nebraska, recently installed a new computer system that allows customers to pay for meals with a bank debit card. The manager of the restaurant claims this new system will decrease the waiting time, and that the probability of getting a meal in under two minutes (with this system in place) is 0.75. Suppose four customers are selected at random. Let the random variable X be the number of customers who receive their meal in under two minutes.
a. Construct the probability distribution for X.
b. Suppose none of the four customers receives their meal in under two minutes. Is there any evidence to suggest the manager’s claim is false? Justify your answer.
Most physicians in Canada graduated from a medical school in Canada. However, some attended medical school in the United States or another foreign country. The probability that a physician in Alberta attended a Canadian medical school is 0.684; in British Columbia, 0.705; in Quebec, 0.891; and in Ontario, 0.736.8 Suppose one physician is independently selected from each province, and let the random variable Y be the number of physicians who attended a Canadian medical school.
a. Construct a probability distribution for Y.
b. What is the probability that at least one physician attended a Canadian medical school?
c. Suppose another group of physicians is selected, one from each province. What is the probability that at least three physicians from each group attended a Canadian medical school?