Download In the table above what are P(A and E ) and P(C | E )? 12/125, 28

1.
In the table above what are P(A and E ) and P(C | E )?
2.
a. 12/125, 28/125
b. 12/63, 28/60
c. 12/125, 28/63
d. 12/125, 28/60
e. 12/63, 28/63
The GPA (grade point average) of students who take the AP Statistics exam are approximately normally distributed
with a mean of 3.4 with a standard deviation of 0.3. Using Table A, what is the probability that a student selected at
random from this group has a GPA lower than 3.0?
a. 0.0918
b. 0.4082
c. 0.9082
d. –0.0918
e. 0
3.
You attend a large university with approximately 15,000 students. You want to construct a 90% confidence interval
estimate, within 5%, for the proportion of students who favor outlawing country music. How large a sample do you
need?
4.
Which of the following are examples of quantitative data?
a. The number of years each of your teachers has taught
b. Classifying a statistic as quantitative or qualitative
c. The length of time spent by the typical teenager watching television in a month
d. The daily amount of money lost by the airlines in the 15 months after the 9/11 attacks
e. The colors of the rainbow
Which of the following are discrete and which are continuous?
a. The weights of a sample of dieters from a weight-loss program
b. The SAT scores for students who have taken the test over the past 10 years
c. The AP Statistics exam scores for the almost 50,000 students who took the exam in 2002
d. The number of square miles in each of the 20 largest states
e. The distance between any two points on the number line
5.
6. This years' statistics class was small (only 15 students). This group averaged 74.5 on the final exam with a sample standard
deviation of 3.2. Assuming that this group is a random sample of all students who have taken statistics and the scores in the
final exam for all students are approximately normally distributed, what is an approximate 95% confidence interval for the
true population mean of all statistics students?
7. One researcher wants to construct a 99% confidence interval as part of a study. A colleague says such a high level isn't
necessary and that a 95% confidence level will suffice. In what ways will these intervals differ?
8. A research study gives a 95% confidence interval for the proportion of subjects helped by a new anti-inflammatory drug as
(0.56, 0.65).
a.
b.
Interpret this interval in the context of the problem.
What is the meaning of "95%" confidence interval as stated in the problem?
9. You want to estimate the proportion of Californians who want outlaw cigarette smoking in all public places. Generally
speaking, by how much must you increase the sample size to cut the margin of error in half?
10. The Mathematics Department wants to estimate within five students, and with 95% confidence, how many students will
enroll in Statistics next year. They plan to ask a sample of eligible students whether or not they plan to enroll in Statistics. Over
the past 5 years, the course has had between 19 and 79 students enrolled. How many students should they sample? (Note:
assuming a reasonably symmetric distribution, we can estimate the standard deviation by Range/4.)
11. A distribution is strongly skewed to the left (like a set of scores on an easy quiz) with a mean of 48 and a standard
deviation of 6. What can you say about the proportion of scores that are between 40 and 56? If the test had an approximately
normal shape, what can you say about the proportion of scores that are between 40 and 56?
12. At a school better known for football than academics (a school its football team can be proud of ), it is known that only
20% of the scholarship athletes graduate within 5 years. The school is able to give 55 scholarships for football. What are the
expected mean and standard deviation of the number of graduates for a group of 55 scholarship athletes?
13. It is known that exercise and diet both influence weight loss. Your task is to conduct a study of the effects of diet on weight
loss. Explain the concept of blocking as it relates to this study.
14. Which of the following is not a common characteristic of binomial and geometric experiments?
a.
b.
c.
d.
e.
There are exactly two possible outcomes: success or failure.
There is a random variable X that counts the number of successes.
Each trial is independent (knowledge about what has happened on previous trials gives you no information
about the current trial).
The probability of success stays the same from trial to trial.
P(success) + P(failure) = 1.
15. A married couple has three children. At least one of their children is a boy. What is the probability that the couple has
exactly two boys?
16. A certain type of pen is claimed to operate for a mean of 190 hours. A random sample of 49 pens is tested, and the mean
operating time is found to be 188 hours with a standard deviation of 6 hours. Construct a 95% confidence interval for the true
mean operating time of this type of pen. Does the company's claim seem justified?
17. Describe the shape of the histograms below:
18. After the Challenger disaster of 1986, it was discovered that the explosion was caused by defective O-rings. The probability
that a single O-ring was defective and would fail (with catastrophic consequences) was 0.003 and there were 12 of them (6
outer and 6 inner). What was the probability that at least one of the O-rings would fail (as it actually did)?
19. Which of the following are properties of the normal distribution? Explain your answers.
a.
b.
c.
d.
e.
It has a mean of 0 and a standard deviation of 1.
Its mean = median = mode.
All terms in the distribution lie within four standard deviations of the mean.
It is bell-shaped.
The total area under the curve and above the horizontal axis is 1.
20. Make a stemplot for the number of home runs hit by Mickey Mantle during his career (from question ?1, the numbers are:
13, 23, 21, 27, 37, 52, 34, 42, 31, 40, 54, 30, 15, 35, 19, 23, 22, 18). Do it first using an increment of 10, then do it again using an
increment of 5. What can you see in the second graph that was not obvious in the first?
21. In the problem above, we considered the home runs hit by Mickey Mantle during his career. The following is a stemplot of
the number of doubles hit by Mantle during his career. What is the interquartile range (IQR) of this data? (Hint: n =18.)
22. The following are the salaries, in millions of dollars, for members of the 2001–2002 Golden State Warriors: 6.2, 5.4, 5.4,
4.9, 4.4, 4.4, 3.4, 3.3, 3.0, 2.4, 2.3, 1.3, .3, .3. Which gives a better "picture" of these salaries, mean-based or median-based
statistics? Explain.
23. Look again at the salaries of the Golden State Warriors, (in millions, 6.2, 5.4, 5.4, 4.9, 4.4, 4.4, 3.4, 3.3, 3.0, 2.4, 2.3, 1.3, .3,
.3). Erick Dampier was the highest paid player at $6.2 million. What sort of raise would he need so that his salary would be an
outlier among these salaries?
24. Approximately 10% of the population of the United States is known to have blood type B. If this is correct, what is the
probability that between 11% and 15%, inclusive, of a random sample of 500 adults will have type B blood?
25. Does the following table represent the probability distribution for a discrete random variable?
26. You are going to do an opinion survey in your school. You can sample 100 students and desire that the sample accurately
reflects the ethnic composition of your school. The school data clerk tells you that the student body is 25% Asian, 8% African
American, 12% Latino, and 55% Caucasian. How could you sample the student body so that your sample of 100 would reflect
this composition and what is such a sample called?
27. In a large population, 55% of the people get a physical examination at least once every two years. An SRS of 100 people are
interviewed and the sample proportion is computed. The mean and standard deviation of the sampling distribution of the
sample proportion are
a.
b.
c.
d.
e.
55, 4.97
0.55, 0.002
55, 2
0.55, 0.0497
The standard deviation cannot be determined from the given information.
28. The following table gives the results of an experiment in which the ages of 525 pennies from current change were
recorded. "0" represents the current year, "1" represents pennies one year old, etc.
Describe the distribution of ages of pennies (remember that the instruction "describe" means to discuss center, spread, and
shape). Justify your answer.
29. The following graph shows the distribution of the heights of 300 women whose average height is 65" and whose standard
deviation is 2.5". Assume that the heights of women are approximately normally distributed. How many of the women would
you expect to be less than 5'2" tall?
30. Consider the experiment of drawing two cards from a standard deck of 52 cards. Let event A = "draw a face card on the
first draw," B = "draw a face card on the second draw," and C = "the first card drawn is a diamond." Are the events A and B
independent? Are the events A and C independent?
31. Given the histogram below, draw, as best you can, the boxplot for the same data.
32. On the first test of the semester, the class average was 72 with a standard deviation of 6. On the second test, the class
average was 65 with a standard deviation of 8. Nathan scored 80 on the first test and 76 on the second. Compared to the rest of
the class, on which test did Nathan do better?
33. Jenny is 5'10" tall and is worried about her height. The heights of girls in the school are approximately normally
distributed with a mean of 5'5" and a standard deviation of 2.6". What is the percentile rank of Jenny's height?
34. Suppose 80% of the homes in Lakeville have a desktop computer and 30% have both a desktop computer and a laptop
computer. What is the probability that a randomly selected home will have a laptop computer given that it has a desktop
computer?
35. A coin is known to be unbalanced in such a way that heads only comes up 0.4 of the time. What is the probability the
first head appears on the 4th toss?
36. The coin of problem #1 is flipped 50 times. Let X be the number of heads. What is:
a. the probability of exactly 20 heads?
b. the probability of at least 20 heads?
37. A binomial random variable X has B(300, 0.2). Describe the sampling distribution of
.
38. A distribution is known to be highly skewed to the left with mean 25 and standard deviation 4. Samples of size 10 are
drawn from this population and the mean of each sample is calculated. Describe the sampling distribution of .
39. What is the probability that a sample of size 35 drawn from a population with mean 65 and standard deviation 6 will
have a mean less than 64?
40. An unbalanced coin has p = 0.6 of turning up heads. Toss the coin three times and let X be the count of heads among the
three coins. Construct the probability distribution for this experiment.
41. The probability of winning a bet on red in roulette is 0.474. The binomial probability of winning money if you play 10
games is 0.31 and drops to 0.27 if you play 100 games. Use a normal approximation to the binomial to estimate your
probability of coming out ahead (that is, winning more than 1/2 of your bets) if you play 1000 times. Justify being able
to use a normal approximation for this situation.
42. Crabs off the coast of Northern California have a mean weight of 2 lbs with a standard deviation of 5 oz. A large trap
captures 35 crabs.
a. Describe the sampling distribution for the average weight of a random sample of 35 crabs taken from this
population.
b. What would the mean weight of a sample of 35 crabs have to be in order to be in the top 10% of all such
samples?
43. The probability that a person recovers from a particular type of cancer operation is 0.7. Suppose 8 people have the
operation. What is the probability that
a. exactly 5 recover?
b. they all recover?
c. at least one of them recovers?
44. A certain type of light bulb is advertised to have an average life of 1200 hours. If, in fact, light bulbs of this type only
average 1185 hours with a standard deviation of 80 hours, what is the probability that a sample of 100 bulbs will have
an average life of at least 1200 hours?
45. Half Moon Bay, California, has an annual pumpkin festival at Halloween. A prime attraction to this festival is a "largest
pumpkin" contest. Suppose that the weights of these giant pumpkins are approximately normally distributed with a mean of
125 pounds and a standard deviation of 18 pounds. Farmer Harv brings a pumpkin that is at the 90% percentile of all the
pumpkins in the contest. What is the approximate weight of Harv's pumpkin?
46. In the casino game of roulette, a ball is rolled around the rim of a circular bowl while a wheel containing 38 slots into
which the ball can drop is spun in the opposite direction from the rolling ball; 18 of the slots are red, 18 are black, and 2 are
green. A player bets a set amount, say $1, and wins $1 (and keeps her $1 bet) if the ball falls into the color slot the player has
wagered on. Assume a player decides to bet that the ball will fall into one of the red slots.
a.
b.
What is the probability that the player will win?
What is the expected return on a single bet of $1 on red?