Download Day06 Ch5 13-17

AP Statistics
1) A restaurant has collected data on its customers’ orders and so has estimated empirical probabilities of what happens after the main
course. It was found that 20% had dessert only, 40% had coffee only, and 30% had both dessert and coffee.
a.
Draw a Venn diagram for this situation.
b.
Make a probability table for these events.
c.
Find the probability of the event “had coffee.” (Hint: be careful: this event includes those who did as well as those who
did not have dessert).
d.
Find the probability of the event “did NOT have dessert.”
e.
Find the probability of the event “neither coffee nor dessert.”
f.
Find the probability of the event “had coffee OR dessert.”
g.
Are the events “had coffee” and “had dessert” mutually exclusive? How do you know?
h.
Find the conditional probability of ordering coffee GIVEN that the customer ordered dessert. In which probability
diagram (part a or b) is this easiest to see?
i.
Are “had dessert” and “had coffee” independent events? How do you know?
j.
Find the conditional probability of ordering dessert GIVEN that the customer ordered coffee.
k.
Find the conditional probability of ordering dessert GIVEN that the customer did not order coffee.
l.
To see if coffee and dessert seem to go well together, compare you answers to parts j and k above. In particular, who is
more likely to order dessert: a customer who orders coffee or one who does not?
2) Assume that chest X-rays for detecting tuberculosis have the following properties. For people having tuberculosis the test will detect
the disease 90 percent of the time. For people not having the disease the test will incorrectly indicate that they have the disease 1% of
the time. Assume that the incidence of tuberculosis is 0.5%. A person is selected at random, given the X-ray test, and the radiologist
reports the presence of tuberculosis. What is the probability that the person in fact has the disease?
3) Suppose that the distribution of net typing rate in words per minute (wpm) for experienced typists can be approximated by a normal
curve with mean of 60 wpm and a standard deviation 15 wpm.
a. What is the probability that a randomly selected typist's net rate is at most 50 wpm? Less than 81 wpm?
b. What is the probability that a randomly selected typist's net rate is between 45 and 90 wpm?
c. Would you be surprised to find a typist in this population whose net rate exceeded 105 wpm?
d. Suppose that two typists are independently selected. What is the probability that both their typing rates exceed 75 wpm?
e. Suppose that special training is to be made available to the slowest 20% of the typists. What typing speeds would qualify
individuals for this training?
4) The following question is based on Univariate data.
(a)
A set of data has a mean of 45.6. What is the mean if 5.0 is added to each score?
(b)
A set of data has a standard deviation of 3.0. What is the standard deviation if 5.0 is added to each score?
(c)
You just completed a calculation for the variance of a set of scores, and you got an answer of –21.3. What do you
conclude?
5) You have torn a tendon and are facing surgery to repair it. The orthopedic surgeon explains the risks to you: Infection occurs in 3%
of such operations, the repair fails in 14%, and both infection and failure occur together in 1%.
a)
Are the events "infection" and "repair failure" independent?
b)
What percent of these operations succeed and are free from infection?
6)
(a) If data is skewed to the left with a mean of 3.4, what can you say about the median?
(b) If the data has a standard deviation of 1.3 and the data is transformed according to the formula x* = 2x – 3, what can you
say about the mean, median, variance and standard deviation?
7) Five percent of all VCRs manufactured by a large electronics company are defective. A quality control inspector randomly selects
three VCRs from the production line.
a)
What is the probability that exactly one of these three VCRs is defective?
b)
Let X be the random variable representing the number of defective VCRs out of a sample of 3. Write the probability
distribution for X.
c)
Make a tree diagram for this situation.
d)
Find the probability that the second VCR is defective, given that the first VCR is defective.
e)
Find the mean and standard deviation of this random variable.
8) The distribution of math SAT scores in a reference population is normal with mean 500 and standard deviation 100. ACT math
scores are normally distributed with mean 18 and standard deviation 6.
a)
If Jane scored 720 on the math SAT, what would be her percentile?
b)
What percentage of students score between 680 and 720 on the math SAT?
c)
What score would someone need if he/she wanted to score at the 80th percentile on the math SAT?
d)
If we select 10 students at random, what is the probability that at least 3 will score higher than the score in part c?
e)
If we select students at random, what is the probability that the first student who scores higher than the score in part c is
the 5th one?
f)
If we select students at random, what is the probability that the first student who scores higher than the score in part c is
within the first 4 selected?
g)
A random sample of 36 students from Jefferson High School had a mean math SAT score 530. Is it correct for the
principal to say that his students are better than the national average?
9) The local bowling league has teams consisting of three bowlers each. The Nyuk-Nyuk team consists of Larry, Curly, and Moe. Their
averages and standard deviations are given in the table below.
(a)
(b)
Player
Mean
Standard Deviation
Larry
235
17
Curly
186
22
Moe
197
11
What is the team average and standard deviation assuming that their scores are independent?
The team has a game tonight but Moe has poked both Larry and Curly in the eye (his usual tactic). What is the
probability that the team will achieve a combined score of less than 595 points assuming that their scores are
independent?