Test 7B
AP Statistics
Name:
Directions: Work on these sheets.
Part
1: Multiple Choice. Circle the letter corresponding to the best
answer.
A psychologist studied the number of
puzzles subjects were able to solve in a five-minute period while listening to
soothing music. Let X be the number of
puzzles completed successfully by a subject.
X had the following distribution:
X 1 2 3 4
Probability 0.2
0.4 0.3 0.1
1. Using
the above data, what is the probability that a randomly chosen subject
completes at least 3 puzzles in the five-minute period while listening to
soothing music?
(a) 0.3
(b) 0.4
(c) 0.6
(d) 0.9
(e) The answer cannot be computed from the
information given.
2. Using
the above data, P(X < 3) is
(a) 0.3
(b) 0.4
(c) 0.6
(d) 0.9
(e) The answer cannot be computed from the
information given.
3. Using
the above data, the mean µ of X is
(a) 2.0
(b) 2.3
(c) 2.5
(d) 3.0
(e) The answer cannot be computed from the
information given.
4.
Which of the following random variables should be considered continuous?
(a) The time it takes for a randomly chosen woman
to run 100 meters
(b) The number of brothers a randomly chosen
person has
(c) The number of cars owned by a randomly chosen
adult male
(d) The number of orders received by a mail order
company in a randomly chosen week
(e) None of the above
Test 8B
A P Statistics Name:
Directions: Work on these sheets. A random digit table is attached.
Part
1: Multiple Choice. Circle the letter corresponding to the best
answer.
1. A
dealer in the Sands Casino in Las Vegas selects 40 cards from a standard deck
of 52 cards. Let Y be the number of red
cards (hearts or diamonds) in the 40 cards selected. Which of the following best describes this setting:
(a) Y
has a binomial distribution with n =
40 observations and probability of success p
= 0.5.
(b) Y
has a binomial distribution with n=40
observations and probability of success p
= 0.5, provided the deck is shuffled well.
(c) Y
has a binomial distribution with n=40
observations and probability of success p
= 0.5, provided after selecting a card it is replaced in the deck and the deck
is shuffled well before the next card is selected.
(d) Y
has a normal distribution with mean p
= 0.5.
2. In
a certain large population, 40% of households have a total annual income of
over $70,000. A simple random sample is
taken of 4 of these households. Let X
be the number of households in the sample with an annual income of over $70,000
and assume that the binomial assumptions are reasonable. What is the mean of X?
(a)
1.6
(b)
28,000
(c) 0.96
(d) 2, since the mean must be an integer
(e)
The answer cannot be computed from the information given.
3. The
probability that a three-year-old battery still works is 0.8. A cassette recorder requires four working
batteries to operate. The state of
batteries can be regarded as independent, and four three-year-old batteries are
selected for the cassette recorder.
What is the probability that the cassette recorder operates?
(a) 0.9984
(b) 0.8000
(c) 0.5904
(d)
0.4096
(e) The answer cannot be computed from the
information given.
4. Twenty
percent of all trucks undergoing a certain inspection will fail the
inspection. Assume that trucks are independently
undergoing this inspection, one at a time.
The expected number of trucks inspected before a truck fails inspection
is
(a) 2
(b) 4
(c) 5
(d)
20
(e) The answer cannot be computed from the
information given.
12. Amarillo Slim, a professional dart player, has an 80% chance of hitting the bullseye on a dartboard with any throw. Suppose that he throws 10 darts, one at a time, at the dartboard.
(a) Find the probability that Slim hits the bullseye exactly six times.
(b) Find the probability that he hits the bullseye at least four times.
(c) Compute the mean and variance of the number of bullseyes in 10 throws.
(d) Find the probability that Slim’s first bullseye occurs on the fourth throw.
(e) Find the probability that it takes Amarillo more than 2 throws to hit the bullseye.
13. Harlan comes to class one day, totally unprepared for a pop quiz
consisting of ten multiple-choice questions. Each question has five answer
choices, and Harlan answers each question randomly.
(a) Find the probability that Harlan guesses more
answers correctly than would be expected by chance.
(b) Find the probability that Harlan’s first
correct answer occurs on or after the fourth question.