Assignment

1). The budgeting process for a southeastern college resulted in expense forecasts for the coming year (in $millions) of $13, $14, $15, $16, and $17. Because the actual expenses are unknown, the following respective probabilities are assigned: .21, .08, .27, .33, and .11.

a). Show the probability distribution for the expense forecast.

b). What is the expected value of the expenses for the coming year?

c). What is the probability that the expenses for the coming year is at least $14 million?

d). What is the probability that the expenses for the coming year is more than $15 million?

e). If income projections for the year are estimated at $15 million, comment on the financial position of the college.

2). Worldwide golf ball sales in 2014 totaled an estimated 765 million golf balls worth $870 million. One reason for such a large number of golf ball purchases is that golfers lose them at the rate of 4.2 per 18-hole round.

a). What is the probability that zero balls will be lost in an 18-hole round?

b). What is the probability that less than 3 balls will be lost in an 18-hole round?

c). What is the probability that at least 7 balls will be lost in a 36-hole round?

d). What is the probability that 10 balls will be lost in a 72-hole round?

3). Ericsson Airlines has a central office that takes reservations for all flights flown by the airline. The calls received during any week have a median of 12,000 and a standard deviation of 2,500.

a). During what percentage of the weeks does the airline receive more than 10,500 phone calls?

b). During what percentage of the weeks does it receive more than 13,800 calls?

c). During what percentage of the weeks does it receive between 12,600 and 13,400 calls?

d). During what percentage of the weeks does the airline receive less than 12,800 or more than 15,600 calls?

e). The lower 20% of phone calls are less than what number of phone calls during a week?

4). A company is going to release four quarterly reports this year. Suppose the company has a 32% chance of beating analyst expectations each quarter.

a). What is the probability that the company beats analyst expectations every quarter of this year?

b). What is the probability the company beats analyst expectations more than half the time this year?

c). What is the expected number of times the company will beat analyst expectations this year? How much is this expected to vary?

d). What is the probability the company will not beat analyst expectations for exactly two quarters?

5). Let x be the larger outcome in a function where a question is asked about how much money a person spent on their new car (in $thousands).

f(x) = (x2 - 1)/658, where x = 2, 5, 8, 10, 13, 17

a). Show the probability distribution for the expense forecast.

b). What is the average dollar amount spent on a new car?

c). What is the probability that a person chose at random spent no more than $9?

d). What is the probability that a person spent $5 or $8?

e). What is the probability that a person spent between $9 and $18, inclusive?

6). A set of final examination grades in an introductory statistics course was found to have a mean of 73 and a standard deviation of 8.

a). What is the probability of getting a grade of an 85 or above on this exam?

b). What percentage of students scored between a 76 and 83?

c). What is the median for this specific exam?

d). Only 8% of the students scored higher than what grade?

e). If the professor grades on a curve (gives A's to the top 10% of the class regardless of the score), are you better off with a grade of 81 on this exam or a grade of 68 on a different exam where the mean is 62 and the standard deviation is 3? Show your answer statistically and explain in one sentence or less.

7). Airline passengers arrive randomly and independently at the passenger-screening facility at a major international airport. The mean arrival rate is 8 passengers per minute.

a). What is the expected number of arrivals per hour? What is the standard deviation of arrival rates per hour?

b). What is the probability that three or fewer passengers arrive in a one-minute period?

c). What is the probability of at least 2 arrivals in a 15-second period?

d). What is the probability of 4 arrivals in a 15-second period?

e). What is the probability of having between 4 and 7 arrivals in a 45-second period, not inclusive?

8). Sixty percent of midsize manufacturers planned to have management representatives visit Canada and Mexico to take advantage of opportunities created by the North American Free Trade Agreement (G-T Survey of American Manufacturers, 2008). An export import group in Toronto, Canada, has invited 20 U.S. midsize manufacturers to participate in a conference to explore trade opportunities.

a). How many companies would you expect not to send representatives?

b). What is the probability that more than 4 companies will not send representatives?

c). What is the probability that exactly 9 companies will send representatives?

d). What is the probability that between 12 and 16 companies will send representatives, not inclusive?

e). What is the probability that exactly 10 companies will not send representatives if 25 U.S. midsize manufacturers were invited?