1. (5 points) In a certain town, 4% of people commute to
work by bicycle. If a person is selected randomly from the town, what are the
odds against selecting someone who commutes by bicycle?
2. (5 points) Among the contestants in a competition are 43
women and 21 men. If 5 winners are randomly selected, what is the probability
that they are all men?
3. (5 points) A tourist in France wants to visit 6 different
cities. If the route is randomly selected, what is the probability that she
will visit the cities in alphabetical order?
4. (5 points) A police department reports that the
probabilities that 0, 1, 2, and 3 burglaries will be reported in a given day
are 0.49, 0.42, 0.06 and 0.03, respectively. What is the mean of the given
5. (5 points) The standard deviation for the binomial
distribution with n=40 and p=0.4 is:
6. (5 points) The probability that a person has immunity to
a particular disease is 0.3. Find the mean number who have immunity in samples
of size 18.
7. (5 points) The incomes of trainees at a local mill are
normally distributed with a mean of $1100 and a standard deviation of $120.
What percentage of trainees earn less than $900 a month?
8. (5 points) For a standard normal distribution, find the
percentage of data that are between 3 standard deviations below the mean and 2
standard deviation above the mean.
SHORT ANSWER. Write the word or phrase that best completes
each statement or answers the question. Express percents as decimals. Round
dollar amounts to the nearest cent.
9. (15 points) Most of us hate buying mangos that are picked
too early. Unfortunately, by waiting until the mangos are almost ripe to pick
carries a risk of having 7% of the picked rot upon arrival at the packing
facility. If the packing process is all done by machines without human
inspection to pick out any rotten mangos, what would be the probability of
having at most 2 rotten mangos packed in a box of 12?
10. We have 7 boys and 3 girls in our church choir. There is
an upcoming concert in the local town hall. Unfortunately, we can only have 5
youths in this performance. This performance team of 5 has to by picked randomly
from the crew of 7 boys and 3 girls.
a. (5 points) What is the probability that all 3 girls are
picked in this team of 5?
b. (5 points) What is the probability that none of the girls
are picked in this team of 5?
c. (5 points) What is the probability that 2 of the girls
are picked in this team of 5?
11. (15 points) A soda company want to stimulate sales in
this economic climate by giving customers a chance to win a small prize for
every bottle of soda they buy. There is a 20% chance that a customer will find
a picture of a dancing banana ( ) at the bottom of the cap upon opening up a
bottle of soda. The customer can then redeem that bottle cap with this picture
for a small prize. Now, if I buy a 6-pack of soda, what is the probability that
I will win something, i.e., at least win a single small prize?
12. (15 points) A department store manager has decided that
dress code is necessary for team coherence. Team members are required to wear
either blue shirts or red shirts. There are 9 men and 7 women in the team. On a
particular day, 5 men wore blue shirts and 4 other wore red shirts, whereas 4
women wore blue shirts and 3 others wore red shirt. Apply the Addition Rule to
determine the probability of finding men or blue shirts in the team.