Homework 3
1) Classify each of the following random variables as discrete or continuous:
a) the number of girls born to a couple who will have three children.
) the number of defects found on an automobile at final inspection.
c) the weight (in ounces) of the sandwich meat placed on a submarine sandwich.
d) the number of inco
ect lab procedures conducted at a hospital during a particular week.
e) the number of customers served during a given day at a drive-through window.
f) the time needed by a clerk to complete a task.
g) the temperature of a pizza oven at a particular time.
2) Consider the following investment outcomes and co
esponding probabilities:
Bad outcome: -40,000 with probability 25%
Ok outcome: 10,000 with probability 70%
Great outcome: 70,000 with probability 5%
What is the expected monetary outcome and standard deviation of monetary outcome for this
investment?
3) We are selling five thousand raffle tickets for $10 each to fundraise for AU. We will give
away one car worth $20,000, two home theatre systems worth $3,000 each, five phones
worth $400 each, and 50 gift certificates for $20 each. If someone buys one ticket, what is
their expected winnings. Don’t forget to subtract the cost of the ticket.
4) Suppose that x is a binomial random variable with n = 5 and p = .3.
a) Calculate p(x) for each value of x.
) Find P(x = 3).
c) Find P(x <= 3).
d) Find P(x < 3).
e) Find P(x >= 4).
f) Find P(x > 2).
5) Thirty percent of all students entering a coffee shop also buy a pastry. Suppose six students
enter the coffee shop and the students make independent purchase decisions. Calculate the
following probabilities:
a) That exactly five students buy a pastry.
) That at least three students buy a pastry.
c) That two or fewer students buy a pastry.
d) That at least one student buys a pastry.
6) A professor claims that 90 percent of all email queries are responded to within 24 hours
(excluding weekends). In order to test this claim, a random sample of 15 students who have
ecently emailed the professor were selected. Find the following probabilities:
a) P(x <= 13).
) P(x > 10).
c) P(x >= 14).
d) P(9 <= x' <=12).
e) P(x <= 9).