Practice Questions Chapter 5-7

Multiple Choice Questions

1. In an experiment involving 80 telephone calls aimed at selling a specific insurance policy, the random variable is the number of sales made. This random variable is categorized as:

   • a. discrete random variable

   • b. continuous random variable

   • c. complex random variable

   • d. None of the answers is correct.

2. The weight of an object, measured in grams, serves as an example of:

   • a. a continuous random variable

   • b. a discrete random variable

   • c. either a continuous or a discrete random variable, depending on the weight of the object

   • d. either a continuous or a discrete random variable depending on the units of measurement

3. The definition of the standard deviation is:

   • a. variance squared

   • b. the square root of the sum of the deviations from the mean

   • c. the same as the expected value

   • d. positive square root of the variance

Exhibit 5-2

The following probability distribution illustrates daily sales at Michael's Co.:

• Daily Sales ($1,000s): Probability40: 0.150: 0.460: 0.370: 0.2

4. From Exhibit 5-2, the expected daily sales amount is:

   • a. $55,000

   • b. $56,000

   • c. $50,000

   • d. $70,000

Exhibit 5-3

The probability distribution detailing the number of goals scored by the Lions soccer team per game is below:

• Number of Goals: Probability0: 0.051: 0.152: 0.353: 0.304: 0.15

5. Based on Exhibit 5-3, the likelihood of the Lions scoring no goals in a game is:

   • a. 0.95

   • b. 0.85

   • c. 0.75

   • d. None of the answers is correct.

Exhibit 5-5

AMR, a computer consulting firm, has the following probability distribution for new clients obtained each month:

• Number of
  New Clients Probability
  0 0.05
  1 0.10
  2 0.15
  3 0.35
  4 0.20
  5 0.10
  6 0.05

  Number of New Clients: Probability0: 0.051: 0.102: 0.153: 0.354: 0.205: 0.106: 0.05

6. In relation to Exhibit 5-5, the variance is:

   • a. 1.431

   • b. 2.0475

   • c. 3.05

   • d. 21

7. Among the characteristics of a binomial experiment, which of the following is true?

   • a. At least two outcomes are possible

   • b. The probability of success varies from trial to trial

   • c. The trials are independent

   • d. All of these answers are correct.

8. The variance for the binomial probability distribution can be expressed as:

   • a. Var(x) = p(1 − p)

   • b. Var(x) = np

   • c. Var(x) = n(1 − p)

   • d. Var(x) = np(1 − p)

9. The standard deviation within a binomial distribution corresponds to:

   • a. E(x) = pn(1 − n)

   • b. E(x) = np(1 − p)

   • c. E(x) = np

   • d. None of the alternative answers is correct.

10. In a binomial experiment characterized by p = 0.5 and a sample size of 100, the expected value is:

• a. 0.50

• b. 0.30

• c. 50

• d. Insufficient information for an answer.

11. Among a class of 100 students, 20% plan to attend graduate school. The corresponding standard deviation for this binomial distribution is:

• a. 20

• b. 16

• c. 4

• d. 2

Exhibit 5-8

In a large university where 60% of the students are female, a random sample of 8 students is chosen.

12. Pertaining to Exhibit 5-8, the variable being examined in this experiment is:

• a. the 60% of female students

• b. the random sample of 8 students

• c. the number of female students from the sample of 8

• d. the size of the student body

Exhibit 5-10

The probability that Pete will catch fish during a fishing expedition is 0.8, and he plans to fish for 3 days next week.

13. According to Exhibit 5-10, the anticipated number of days Pete will successfully catch fish is:

• a. 0.6

• b. 0.8

• c. 2.4

• d. 3

Additional Questions

14. The binomial probability distribution achieves maximum symmetry when:

• a. n is 30 or greater

• b. n equals p

• c. p approaches 1

• d. p equals 0.5

15. For any continuous random variable, the probability of it taking on a specific value is:

• a. 1.00

• b. 0.50

• c. any value between 0 to 1

• d. zero

16. The peak of a normal curve occurs at:

• a. one standard deviation right of the mean

• b. two standard deviations right of the mean

• c. approximately three standard deviations right of the mean

• d. the mean

17. The standard deviation for a standard normal distribution:

• a. is always zero

• b. is always one

• c. can be any positive value

• d. can be any value

18. If Z is a standard normal random variable, then P(-1.5 ≤ z ≤ 1.09) equals:

• a. 0.4322

• b. 0.3621

• c. 0.7953

• d. 0.0711

19. For a standard normal random variable z, what is its value if the area to the right is 0.1112?

• a. 0.3888

• b. 1.22

• c. 2.22

• d. 3.22

20. In a standard normal random variable z, what is its value where the area to the right equals 0.1401?

• a. 1.08

• b. 0.1401

• c. 2.16

• d. -1.08

21. For a standard normal distribution, the probability of obtaining a z value less than 1.6 is:

• a. 0.1600

• b. 0.0160

• c. 0.0016

• d. 0.9452

Exhibit 6-5

The weight of items produced by a machine is normally distributed with a mean of 8 ounces and a standard deviation of 2 ounces.

22. According to Exhibit 6-5, the random variable in this case refers to:

• a. the weight of items produced by the machine

• b. 8 ounces

• c. 2 ounces

• d. the normal distribution

23. In relation to Exhibit 6-5, what percentage of the items will weigh between 6.4 and 8.9 ounces?

• a. 0.1145

• b. 0.2881

• c. 0.1736

• d. 0.4617

Exhibit 6-6

The life expectancy of a specific tire brand is normally distributed, with a mean of 40,000 miles and a standard deviation of 5,000 miles.

24. Referring to Exhibit 6-6, the variable being assessed in this experiment is:

• a. the life expectancy of this tire brand

• b. the normal distribution

• c. 40,000 miles

• d. None of the alternative answers is correct.

25. From Exhibit 6-6, what is the probability that a randomly selected tire will last exactly 47,500 miles?

• a. 0.4332

• b. 0.9332

• c. 0.0668

• d. zero

26. The term for standard deviation in relation to proportion is:

• a. standard proportion

• b. sample proportion

• c. average proportion

• d. standard error of the proportion

27. The standard deviation in relation to the mean is termed:

• a. standard x

• b. standard error of the mean

• c. sample standard mean

• d. sample mean deviation

28. A simple random sample of size n from a finite population of size N must be selected so that each possible sample of size:

• a. N has equal selection probability

• b. n has a 0.5 probability

• c. n has a 0.1 probability

• d. n has the same probability of being selected

29. If a population contains 500 elements, the probability of selecting an element in a simple random sample of 50 on the first draw is:

• a. 0.100

• b. 0.010

• c. 0.001

• d. 0.002

30. A simple random sample of size n drawn from a finite population of size N must have:

• a. same probability of being selected

• b. a probability of 1/n of being selected

• c. a probability of 1/N of being selected

• d. a probability of N/n of being selected

31. A simple random sample from a process (infinite population) is selected under the condition that:

• a. each element belongs to the same population

• b. each element is drawn independently

• c. each element comes from the same population and is drawn independently

• d. probabilities for selection can vary

32. Among the following, which represents a point estimator(s)?

• a. σ

• b. μ

• c. s

• d. All of these answers are correct.

Exhibit 7-2

In a survey of 400 registered voters regarding potential changes to gun laws, 300 said "yes," and 100 said "no."

33. According to Exhibit 7-2, the point estimate of the proportion in the population responding "yes" is:

• a. 300

• b. approximately 300

• c. 0.75

• d. 0.25

Exhibit 7-3

Data gathered from a simple random sample includes the following numbers: 16, 19, 18, 17, 20, 18.

34. Referring to Exhibit 7-3, the point estimate of the population mean is:

• a. 18.0

• b. 19.6

• c. 108

• d. sixteen, since 16 is the smallest value in the sample

35. The expected value for the random variable is:

• a. σ

• b. the standard error

• c. the sample size

• d. μ

36. Within a population of 500 elements, a sample of 225 is drawn. Knowing that the population's variance is 900, the standard error of the mean is approximately:

• a. 1.1022

• b. 2

• c. 30

• d. 1.4847

37. Doubling the sample size will:

• a. reduce the standard error of the mean to half its current value

• b. reduce the standard error of the mean to about 70% of its current value

• c. have no impact on the standard error of the mean

• d. double the standard error of the mean

38. With a population mean of 84 and standard deviation of 12, the probability that the sample mean falls between 80.54 and 88.9 with a sample size of 36 is:

• a. 0.0347

• b. 0.7200

• c. 0.9511

• d. None of the alternative answers is correct.

Exhibit 7-4

A simple random sample of 121 cologne bottles showed an average content of 4 ounces, with a known population standard deviation of 0.22 ounces.

39. According to Exhibit 7-4, the standard error of the mean is:

• a. 0.3636

• b. 0.0331

• c. 0.0200

• d. 4.000

1. In an experiment involving 80 telephone calls aimed at selling a specific insurance policy, the random variable is the number of sales made. This random variable is categorized as: a. discrete random variable b. continuous random variable c. complex random variable d. None of the answers is correct.

2. The weight of an object, measured in grams, serves as an example of: a. a continuous random variable b. a discrete random variable c. either a continuous or a discrete random variable, depending on the weight of the object d. either a continuous or a discrete random variable depending on the units of measurement

3. The definition of the standard deviation is: a. variance squared b. the square root of the sum of the deviations from the mean c. the same as the expected value d. positive square root of the variance

4. From Exhibit 5-2, the expected daily sales amount is: a. $55,000 b. $56,000 c. $50,000 d. $70,000

5. Based on Exhibit 5-3, the likelihood of the Lions scoring no goals in a game is: a. 0.95 b. 0.85 c. 0.75 d. None of the answers is correct.

6. In relation to Exhibit 5-5, the variance is: a. 1.431 b. 2.0475 c. 3.05 d. 21

7. Among the characteristics of a binomial experiment, which of the following is true? a. At least two outcomes are possible b. The probability of success varies from trial to trial c. The trials are independent d. All of these answers are correct.

8. The variance for the binomial probability distribution can be expressed as: a. Var(x) = p(1 − p) b. Var(x) = np c. Var(x) = n(1 − p) d. Var(x) = np(1 − p)

9. The standard deviation within a binomial distribution corresponds to: a. E(x) = pn(1 − n) b. E(x) = np(1 − p) c. E(x) = np d. None of the alternative answers is correct.

10. In a binomial experiment characterized by p = 0.5 and a sample size of 100, the expected value is: a. 0.50 b. 0.30 c. 50 d. Insufficient information for an answer.

11. Among a class of 100 students, 20% plan to attend graduate school. The corresponding standard deviation for this binomial distribution is: a. 20 b. 16 c. 4 d. 2

12. Pertaining to Exhibit 5-8, the variable being examined in this experiment is: a. the 60% of female students b. the random sample of 8 students c. the number of female students from the sample of 8 d. the size of the student body

13. According to Exhibit 5-10, the anticipated number of days Pete will successfully catch fish is: a. 0.6 b. 0.8 c. 2.4 d. 3

14. The binomial probability distribution achieves maximum symmetry when: a. n is 30 or greater b. n equals p c. p approaches 1 d. p equals 0.5

15. For any continuous random variable, the probability of it taking on a specific value is: a. 1.00 b. 0.50 c. any value between 0 to 1 d. zero

16. The peak of a normal curve occurs at: a. one standard deviation right of the mean b. two standard deviations right of the mean c. approximately three standard deviations right of the mean d. the mean

17. The standard deviation for a standard normal distribution: a. is always zero b. is always one c. can be any positive value d. can be any value

18. If Z is a standard normal random variable, then P(-1.5 ≤ z ≤ 1.09) equals: a. 0.4322 b. 0.3621 c. 0.7953 d. 0.0711

19. For a standard normal random variable z, what is its value if the area to the right is 0.1112? a. 0.3888 b. 1.22 c. 2.22 d. 3.22

20. In a standard normal random variable z, what is its value where the area to the right equals 0.1401? a. 1.08 b. 0.1401 c. 2.16 d. -1.08

21. For a standard normal distribution, the probability of obtaining a z value less than 1.6 is: a. 0.1600 b. 0.0160 c. 0.0016 d. 0.9452

22. According to Exhibit 6-5, the random variable in this case refers to: a. the weight of items produced by the machine b. 8 ounces c. 2 ounces d. the normal distribution

23. Referring to Exhibit 6-5, what percentage of the items will weigh between 6.4 and 8.9 ounces? a. 0.1145 b. 0.2881 c. 0.1736 d. 0.4617

24. Referring to Exhibit 6-6, the variable being assessed in this experiment is: a. the life expectancy of this tire brand b. the normal distribution c. 40,000 miles d. None of the alternative answers is correct.

25. From Exhibit 6-6, what is the probability that a randomly selected tire will last exactly 47,500 miles? a. 0.4332 b. 0.9332 c. 0.0668 d. zero

26. The term for standard deviation in relation to proportion is: a. standard proportion b. sample proportion c. average proportion d. standard error of the proportion

27. The standard deviation in relation to the mean is termed: a. standard x b. standard error of the mean c. sample standard mean d. sample mean deviation

28. A simple random sample of size n from a finite population of size N must be selected so that each possible sample of size: a. N has equal selection probability b. n has a 0.5 probability c. n has a 0.1 probability d. n has the same probability of being selected

29. If a population contains 500 elements, the probability of selecting an element in a simple random sample of 50 on the first draw is: a. 0.100 b. 0.010 c. 0.001 d. 0.002

30. A simple random sample of size n drawn from a finite population of size N must have: a. same probability of being selected b. a probability of 1/n of being selected c. a probability of 1/N of being selected d. a probability of N/n of being selected

31. A simple random sample from a process (infinite population) is selected under the condition that: a. each element belongs to the same population b. each element is drawn independently c. each element comes from the same population and is drawn independently d. probabilities for selection can vary

32. Among the following, which represents a point estimator(s)? a. σ b. μ c. s d. All of these answers are correct.

33. According to Exhibit 7-2, the point estimate of the proportion in the population responding "yes" is: a. 300 b. approximately 300 c. 0.75 d. 0.25

34. Referring to Exhibit 7-3, the point estimate of the population mean is: a. 18.0 b. 19.6 c. 108 d. sixteen, since 16 is the smallest value in the sample

35. The expected value for the random variable is: a. σ b. the standard error c. the sample size d. μ

36. Within a population of 500 elements, a sample of 225 is drawn. Knowing that the population's variance is 900, the standard error of the mean is approximately: a. 1.1022 b. 2 c. 30 d. 1.4847

37. Doubling the sample size will: a. reduce the standard error of the mean to half its current value b. reduce the standard error of the mean to about 70% of its current value c. have no impact on the standard error of the mean d. double the standard error of the mean

38. With a population mean of 84 and standard deviation of 12, the probability that the sample mean falls between 80.54 and 88.9 with a sample size of 36 is: a. 0.0347 b. 0.7200 c. 0.9511 d. None of the alternative answers is correct.

39. According to Exhibit 7-4, the standard error of the mean is: a. 0.3636 b. 0.0331 c. 0.0200 d. 4.000