The time in minutes for which a student uses a computer terminal at the computer center of a major university follows an exponential probability distribution with a mean of 36 minutes. Assume a student arrives at the terminal just as another student is beginning to work on the terminal.
a. What is the probability that the wait for the second student will be 15 minutes or less (to 4 decimals)?
b. What is the probability that the wait for the second student will be between 15 and 45 minutes (to 4 decimals)?
Sparagowski & Associates conducted a study of service times at the drive-up window of fast-food restaurants. The average service time at McDonald's restaurants was 2.78 minutes (The Cincinnati Enquirer, July 9, 2000). Service times such as these frequently follow an exponential distribution.Round your answers to 4 decimal places.
a. What is the probability that a customer's service time is more than 2.78 minutes?
The time needed to complete a final examination in a particular college course is normally distributed with a mean of 77 minutes and a standard deviation of 12 minutes. Answer the following questions.
a. What is the probability of completing the exam in one hour or less (to 4 decimals)?
b. What is the probability that a student will complete the exam in more than 60 minutes but less than 75 minutes (to 4 decimals)?
c. Assume that the class has 60 students and that the examination period is 90 minutes in length. How many students do you expect will be unable to complete the exam in the allotted time (0 decimals)?
Suppose we are interested in bidding on a piece of land and we know one other bidder is interested. The seller announced that the highest bid in excess of $10,500 will be accepted. Assume that the competitor's bid x is a random variable that is uniformly distributed between $10,500 and $14,500.
a. Suppose you bid $12,000. What is the probability that your bid will be accepted (to 2 decimals)?
b. Suppose you bid $14,000. What is the probability that your bid will be accepted (to 2 decimals)?
c. What amount should you bid to maximize the probability that you get the property (in dollars)?
d. Suppose that you know someone is willing to pay you $16,000 for the property. You are considering bidding the amount shown in part (c) but a friend suggests you bid $13,250. If your objective is to maximize the expected profit, what is your bid?
What is the expected profit for this bid (in dollars)?
According to the Sleep Foundation, the average night's sleep is 6.8 hours (Fortune, March 20, 2006). Assume the standard deviation is .6 hours and that the probability distribution is normal.
a. What is the probability that a randomly selected person sleeps more than 8 hours (to 4 decimals)?
b. Doctors suggest getting between 7 and 9 hours of sleep each night. What percentage of the population gets this much sleep (0 decimals)?
The average travel time to work for New York City residents is 36.5 minutes (Time Almanac, 2001). Assume that the exponential probability distribution applies.
a. Which of the following functions is the probability density function for travel time to work?
b. What is the probability it will take a typical New Yorker between 20 and 40 minutes to travel to work (to 4 decimals)?
c. What is the probability it will take a typical New Yorker more than 40 minutes to travel to work (to 4 decimals)?
The average amount of precipitation in Dallas, Texas, during the month of April is 3.5 inches (The World Almanac, 2000). Assume that a normal distribution applies and that the standard deviation is .8 inches.
a. What percentage of the time does the amount of rainfall in April exceed 5 inches (to 2 decimals)?
b. A month is classified as extremely wet if the amount of rainfall is in the upper 10% for that month. How much precipitation must fall before a month of April is classified as extremely wet (in inches, to 2 decimals)?
Delta Airlines quotes a flight time of 2 hours, 5 minutes for its flights from Cincinnati to Tampa. Suppose we believe that actual flight times are uniformly distributed between 2 hours and 2 hours, 20 minutes
a. What is the probability that the flight will be no more than 5 minutes late?
b. What is the probability that the flight will be more than 10 minutes late?
c. What is the expected flight time, in minutes?