BUS 273 - Problem Sheet #7
Q1. Forest Green Brown, Inc., produces bags of cypress mulch. The weight in pounds per bag varies,
as indicated in the accompanying table.
a) Graph the probability distribution.
b) Calculate and graph the cumulative probability distribution.
c) What is the probability that a randomly chosen bag will contain more than 45 and less than
49 pounds of mulch?
d) Compute the mean and standard deviation of the weight per bag.
e) The cost (in cents) of producing a bag of mulch is 75 + 2X, where X is the number of pounds
per bag. The revenue from selling the bag, regardless of weight, is $2.50. If profit is defined
as the difference between revenue and cost, find the mean and standard deviation of profit
per bag.
Q2. A company installs new central-heating furnaces and has found that for 15% of all installations, a
return visit is needed to make some modifications. Six installations were made in a particular week.
Assume independence of outcomes for these installations.
a) What is the probability that a return visit will be needed in all these cases?
b) What is the probability that a return visit will be needed in none of these cases?
c) What is the probability that a return visit will be needed in more than 1 of these cases?
Cumulative Distribution Function
Binomial with n = 6 and p = 0.1500000
x P( X <= x )
0.00 0.37715
1.00 0.77648
2.00 0.95266
3.00 0.99411
4.00 0.99960
5.00 0.99999
6.00 1.00000
Q3. A small commuter airline flies planes that can seat up to 8 passengers. The airline has
determined that the probability that a ticketed passenger will not show up for a flight is 0.2. For each
flight the airline sells tickets to the first 10 people placing orders. The probability distribution for the
number of tickets sold per flight is shown in the accompanying table. For what proportion of the
airline’s flights does the number of ticketed passengers showing up exceed the number of available
seats? (Assume independence between the number of tickets sold and the probability that a ticketed
passenger will show up.)
