Download Name: Per: ______ Date: ______ AP Statistics Chapters 7 and 8

Name: ___________________________
Per: ___________
Date: __________
AP Statistics Chapters 7 and 8 Test Review
1.
What is a continuous random variable? What is a discrete random variable?
2. Mr. Miguel has a distribution of grades (A=4, B=3, and so on) in a large as
Grade:
Probability:
0
.01
1
.05
2
.30
3
.43
4
.21
Find the average (that is, the mean) grade in this course.
3. A random variable X has a probability distribution as follows:
X
P(X)
0
k
1
2k
2
8k
3
4k
Then the probability that P(X=3) is equal to?
4. What is the Law of Large Numbers? What does it mean?
5. A university claims that 80% of its football players get degrees. An investigation examines the
fate of all 20 players who entered the program over a period of several years that ended six
years ago. Of these players, 11 graduated and the remaining 9 are no longer in school. If the
university’s claim is true, the number of players among the 20 who graduate should have the
binomial distribution with 𝑛 = 20 and 𝑝 = .8. What is the mean number of graduates out of 20
players?
6. In some cultures, it is considered very important to have a son to carry on the family name.
Suppose that a couple in one of these cultures plans to have children until they have exactly one
son. Find the average number of children per family in such a culture.
7. If we were to draw a card from a deck, observe the card, replace the card within the deck, and
count the number of times we draw a card until we observe a jack, find the probability that X=4.
8. The State Department is trying to identify an individual who speaks Farsi to fill a foreign
embassy position. They have determined that 4% of the applicant pool are fluent in Farsi. What
is the probability that they will have to interview more than 25 until they find one who speaks
Farsi? More than 40?
9. The count X of children with type O blood among 5 children whose parents carry genes for both
the O and the A blood types is 𝐵(5, .25). Find 𝑃(𝑋 = 3).
10. Suppose that Jack guesses on each question of a 50-item true-false quiz. Find the probability
that Jack passes if a score of above 30 is needed to pass.
Free Response:
11. Patients receiving artificial hips often experience pain after surgery. The pain is measured on a
subjective scale with possible values of 1 to 5. Assume that X is a random variable representing
the pain score for a randomly elected patient. The following table gives part of the probability
distribution for X.
X
P(X)
a.)
b.)
c.)
d.)
1
.1
2
3
.2
Find P(X = 2)
Find the probability that the pain score is less than 4.
Find the probability that the pain score is greater than 3.
Find the mean for this distribution
4
.3
5
.3
12. A quarterback completes 68% of his passes.
a. What is the probability that the quarterback throws 5 incomplete passes before he has a
completion?
b. What is the probability that the quarterback throws his first completion in no more than
5 attempts?
c. How many passes, on average, can the quarterback expect to throw before he
completes his first pass?
d. Use two methods to determine the probability that it takes more than 9 attempts
before he completes a pass.
13. A cold remedy is said to be 88% effective in curing cold symptoms. An investigator tests this
remedy on 12 randomly selected patients suffering from a common cold.
a. Find the probability that the remedy works for 11 of the patients.
b. Find the probability that the remedy works for more than 7 of the patients.
c. Find the probability that the remedy works for less than half of the patients.
d. What is the expected value for the number of people in the experiment who have
success with the remedy?