Solve the following problems:
Q1 An investment can lead to a profit of $10,000, $5,000, $4,000, and $1,000, with respective probabilities of .4, .3, .2, and .05. In addition, there is a 3 percent chance of breaking even and a small chance of losing $10,000. Find the expected profit.
Q2 A car dealership has combined all popular options available in four packages. The first three packages have the same chance of being sold and the fourth package is twice as likely to be sold as any one of the other packages. If package 1, package 2, and package 4 contain a CD player, find the probability that a randomly selected car will be sold with a CD player. Now assume that five different customers have ordered cars independently, what is the probability that at least 3 CD players will be ordered?
Q3 Average occupancy rate at the Full Moon Motel is about 40 percent. It has 15 rooms. Assuming binomial distribution, find the probability that on any given day
a) exactly 6 rooms will be occupied
b) at least 3 rooms will be occupied
c) no more than 9 rooms will be occupied
d) the motel will be full
Q4The average number of customer complaints at the Full Moon Motel is five per day. Find the probability that on a typical day, the motel will receive
a) eight complaints
b) at least two complaints
Q5 Demand for a product is normal, with mean being 400 and standard deviation being 25 units. Find
a) Pr (demand > 445)
b) Pr (demand is between 375 and 425)
c) Pr (demand equals 400)
d) Pr (demand exceeds 500)
e) The 5 percentile demand level
Q6 The sales of a product are uniformly distributed between 300 and 800. Find
a) Probability (Sales < 500)
b) Probability (Sales between 700 and 900)
c) Probability of sales exactly equal to 750
d) 15 percentile sales level
Q7 The average life of a light bulb is 500 hours. Find
a) the probability that a bulb will last more than 1,000 hours
b) the probability that a bulb will last less than 100 hours
c) the median life
d) the probability that a bulb will last exactly 500 hours
e) the 95 Percentile
Q8 An elevator has a design capacity of 2,560 pounds and a posted limit of 16 passengers. The weight of adults is approximately normal with a mean of 150 pounds and standard deviation of 20 pounds. Find the probability that the elevator will be overloaded if 16 people are in the elevator. How many passengers would you recommend if you wanted to be sure that the overloading probability is less than 0.001?