AP STATS REVIEW SESSION 3: PROBABILITY Name: ______

1.) According to a CBS/New York Times poll taken in 1992, 15% of the public have responded to a telephone call-in poll. In a random group of five people, what is the probability that exactly two have responded to a call-in poll

  1. .138
  2. .165
  3. .300
  4. .835
  5. .973

2.)The yearly mortality rate for American men from prostate cancer has been constant for decades at about 25 of every 100,000 men. In a group of 100 American men, what is the probability that at least 1 will die from prostate cancer?

  1. .00025
  2. .0247
  3. .025
  4. .9753
  5. .99975

3.)For an advertising promotion, and auto dealer hands out 1000 lottery tickets with a proze of a new car worth $25,000. For someone with a single ticket, what is the standard deviation for the amount won?

  1. $7.07
  2. $25.00
  3. $49.95
  4. $790.17
  5. 624,375

4.)Suppose that among 6000 students at a high school, 1500 are taking honors courses and 1800 prefer watching basketball to watching football. If taking honors courses and preferring basketball are independent, how many students are both taking honors courses and prefer basketball to football?

  1. 300
  2. 330
  3. 450
  4. 825
  5. There is insufficient information to answer this question

5.)Suppose that, in a certain part of the world, in any 50-year period the probability of a major plague is .39, the probability of a major famine is .52, and the probability of both a plague and a famine is .15. What is the probability of a famine given that there is a plague?

  1. .240
  2. .288
  3. .370
  4. .385
  5. .760

6.)Suppose that, for any given year, the probabilities that the stock market declines, that women’s hemlines are lower, and that both events occur are, respectively, .4, .35, and .3. Are the two events independent?

  1. Yes, because (.4)(.35)≠.3
  2. No, because (.4)(.35)≠.3
  3. Yes, because .4 > .35 > > .3
  4. No, because .5(.3 + .4) = .35
  5. There is insufficient information to answer this question

7.)If P(A) = .2 and P(B) = .1, what is P( A U B) if A and B are independent?

  1. .02
  2. .28
  3. .30
  4. .32
  5. There is insufficient information to answer this question

8.)Suppose that 2% of a clinic’s patients are known to have cancer. A blood test is developed that is positive in 98% of patients with cancer but is also positive in 3% of patients who do not have cancer. If a person who is chosen at random from the clinic’s patients is given the test and it comes out positive, what is the probability that the person actually has cancer?

  1. .02
  2. .4
  3. .5
  4. .6
  5. .98

9.)Suppose we have a random variable X where the probability associated with the value. What is the mean of X?

  1. .37
  2. .63
  3. 3.7
  4. 6.3
  5. None of the above

10.)Following are parts of the probability distributions for the random variables X and Y.

x / P(x)
1 / ?
2 / .2
3 / .3
4 / ?

If X and Y are independent and the joint probability P( X = 1, Y, = 2) = .1, what is P(X = 4)?

A.).1

B.).2

C.).3

D.).4

E.).5

11.) Suppose X and Y are random variables with E(X) = 25, var(X) = 3, E(Y) = 30, and var(Y) = 4. What are the expected value and variance of the random variable X + Y?

A.)E(X + Y) = 55; var(X + Y) = 3.5

B.)E(X + Y) = 55; var(X + Y) = 5

C.)E(X + Y) = 55; var(X + Y) = 7

D.)E(X + Y) = 27.7; var(X + Y) = 7

E.)There is insufficient information to answer this question.

12.)Suppose X and Y are random variables with µx =10, x=3, µy =15, and y=4. Given that X and Y are independent, what are the mean and standard deviation of the random variable X + Y?

  1. µx + y =25, x + Y =3.5
  2. µx + y =25, x + Y =5
  3. µx + y =25, x + Y =7
  4. µx + y =12.5, x + Y =7
  5. There is insufficient information to answer this question.

13.)Suppose the average height of policemen is 71 inches with a standard deviation of 4 inches, while the average for policewomen is 66 inches with a standard deviation of 3 inches. If a committee looks at all ways of pairing up one make with one female officer, what will be the mean and standard deviation for the difference in heights for the set of possible partners?

  1. Mean of 5 inches with a standard deviation of 1 inch
  2. Mean of 5 inches with a standard deviation of 3.5 inches
  3. Mean of 5 inches with a standard deviation of 5 inches
  4. Mean of 68.5 inches with a standard deviation of 1 inch
  5. Mean of 68.5 inches with a standard deviation of 3.5 inches

14.)Assume the given distribution is Normal. A factory dups an average of 2.43 tons of pollutants into a river every week. If the standard deviation of 0.88 tons, what is the probability that in a week more than 3 tons are dumped?

  1. .2578
  2. .2843
  3. .6500
  4. .7157
  5. .7422

15.)Assume the given distribution is Normal. An electronic product takes an average of 3.4 hours to move through an assembly line. If the standard deviation is 0.5 hour, what is the probability that an item will take between 3 and 4 hours?

  1. .2119
  2. .2295
  3. .3270
  4. .3811
  5. .6730

16.)Assume the given distribution is Normal. The average noise level in a restaurant is 30 decibels with a standard deviation of 4 decibels. 99% of the time it is below what value?

  1. 20.7
  2. 32.0
  3. 33.4
  4. 37.8
  5. 39.3

17.)One company produces movie trailers with mean 150 seconds and standard deviation 40 seconds, while a second company produces trailers with a mean 120 seconds and standard deviation 30 seconds. What is the probability that two randomly selected trailers, one produced by each company, will combine to less than three minutes? Assume the given distributions are Normal.

  1. .000
  2. .036
  3. .099
  4. .180
  5. .405

18.)Assume the given distribution is Normal. Cucumbers grown on a certain farm have weights with a standard deviation of 2 ounces. What is the mean weight of 85% of the cucumbers weigh less than 16 ounces?

  1. 13.92
  2. 14.30
  3. 14.40
  4. 14.88
  5. 15.70

19.)Given that 10% of the nails made using a certain manufacturing process have a length less than 2.48 inches, while 5% have a length greater than 2.54 inches, what are the mean and standard deviation of the lengths of nails? Assume that lengths have a normal distribution.

  1. µ = 2.506,  = 0.0205
  2. µ = 2.506,  = 0.0410
  3. µ = 2.516,  = 0.0825
  4. µ = 2.516,  = 0.1653
  5. The mean and standard deviation cannot be computed from the information given.

20.)Which of the following is an incorrect statement?

  1. The sampling distribution of has mean equal to the population mean µ even if the population is not normally distributed
  2. The sampling distribution of has standard deviation even if the population is not normally distributed
  3. The sampling distribution of is normal if the population has a normal distribution
  4. When n is large, the sampling distribution of is approximately normal even if the population is not normally distributed.
  5. The larger the value of the sample size n, the closer the standard deviation of the sampling distribution of is to the standard deviation of the population

21.)Which of the following is a true statement?

  1. The sampling distribution of has a mean equal to the population proportion p.
  2. The sampling distribution of has a standard deviation equal to
  3. The sampling distribution of has a standard deviation which becomes larger as the sample size becomes larger
  4. The sampling distribution of is considered close to normal provided that n≥30
  5. The sampling distribution of is always close to normal

22.)The ages of people who dies last year in the United States is skewed left. What happens to the sampling distribution of sample means as the sample size goes from n = 50 to n = 200?

  1. The mean gets closer to the population mean, the standard deviation stays the same, and the shape becomes more skewed left
  2. The mean gets closer to the population mean, the standard deviation becomes smaller, and the shape becomes more skewed left
  3. The mean gets closer to the population mean, the standard deviation stays the same, and the shape becomes closer to normal
  4. The mean gets closer to the population mean, the standard deviation becomes smaller, and the shape becomes closer to normal
  5. The mean stays the same, the standard deviation becomes smaller, and the shape becomes closer to normal

23.)Which of the following are unbiased estimators for the corresponding population parameters?

  1. Sample means
  2. Sample proportions
  3. Difference of sample means
  4. Difference of sample proportions
  1. None are unbiased
  2. I and II
  3. I and III
  4. III and IV
  5. All are biased

24.) Suppose that 35% of all business executives are willing to switch companies if offered a higher salary. If a headhunter randomly contacts an SRS of 100 executives, what is the probability that over 40% will be willing to switch companies if offered a higher salary?

  1. .1469
  2. .1977
  3. .4207
  4. .8023
  5. .8531

25.)The average number of daily emergency room admissions at a hospital is 85 with a standard deviation of 37. In a simple random sample of 30 days, what is the probability that the mean number of daily emergency admissions is between 75 and 95?

  1. .1388
  2. .2128
  3. .8612
  4. .8990
  5. .9970

26.)FREE RESPONSE:

ANSWER:

SCORING:

Part (a) is essentially correct for correctly calculating both the mean and median.

Part (a) is partially correct for correctly calculating one of these two measures.

Part (b) is essentially correct for noting that the mean is greater than the median and relating this to the skew

Part (c) is essentially correct for recognizing this as a binomial probability calculation and making the correct calculation.

Part (c) is partially correct for recognizing this as a binomial probability calculation, but with an error such as 1 – (.05)4 or 4(.05)(.95)3

Part (d) is essentially correct for “approximately normal,” = 4.27 and = 01823, and partially correct for two of these three answers.

4: four essentially correct answers

3: three essentially correct answers

2: two essentially correct answers

1: one essentially correct answer