Calculus and Above

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-1, 0, 2, 3, 7...

Use the following sample data to answer questions 1 through 4:

-1, 0, 2, 3, 7, 10, 10

_____1. The mean, X , of the data above is (to the nearest 1/10)

a. 8.3 b. 9.0 c. 9.4 d. 4.4

_____2. The median of the data above is

a. 5 b. 7 c. 10 d. 3

_____3. The mode of the data above is

a. 8.3 b. 10 c. 5 d. 7

_____4. The standard deviation of the data above is (to the nearest 1/10)

a. 5.0 b. 5.3 c. 6.3 d. 4.6

The table below shows the frequency distribution for 10 students on a test with a maximum score of 12. Use these sample data to answer questions 5 through 7:

Score Frequency

1-3 4

4-6 3

7-9 2

10-12 1

______5. The mean score, X , of the data in the frequency distribution above is (to the nearest 1/10)

a. 5.0 b. 5.3 c. 5.4 d. answer not listed

______6. The standard deviation of the scores in the frequency distribution above is (to the nearest 1/10)

a. 1.8 b. 3.0 c. 3.2 d. answer not listed

_____7. The median score lies in which score interval?

a. 1 – 3 b. 4 – 6 c. 7 - 9 d. 10 - 12

_____8. A delivery truck must make stops in eight different cities, designated by the first letter in the name of the city: A, B, C, D, E, F, G, and H. If the order in which the truck visits the eight locations is chosen randomly, what is the probability that it will visit them in alphabetical order? (HINT: Let A = number of ways the truck can visit the eight locations in alphabetical order and B = total number of ways the truck can visit the eight locations, find A/B)

a. 8C1/8P1

b. 1/8P8

c. 1/8C8

d. answer not listed

_____9. A jar contains 12 marbles, 5 of which are blue and 7 of which are red. If 4 marbles are chosen at random and without replacement, what is the probability of selecting 3 blue ones and 1 red one? (HINT: First, Determine how many ways to select 3 blue marbles AND 1 red marble. Then, determine how many total ways to select 4 marbles)

a. (5C3 * 7C1) / 12C4

b. (5P3 * 7P1) / 12P4

c. (5C2 * 7P2) / 12

d. answer not listed

_____10. Suppose that P(A| B) = P(A) , P(Aand B)=.36 , and P(A)=.9 . What is P(B) ? (HINT: Use Formal Multiplication Rule and Intuitive Multiplication Rule)

a. 0.004 b. 0.04 c. 0.4 d. answer not listed

For questions 11 through 13 use the table immediately below. The table shows the number of students who are taking a statistics course in the traditional face-to-face mode versus online by sex. Assume one person is chosen at random from the 220.

Online Traditional Totals

Male 30 60 90

Female 40 90 130

Totals 70 150 220

_____11. If a student taking the course online is chosen at random, the probability that the person is male is

a. 3/22 b. 9/22 c. 1/3 d. 3/7

_____12. If a male is chosen at random, the probability that he is taking the course in the traditional mode is

a. 7/22 b. 2/3 c. 2/5 d. answer not listed

_____13. The events of “choosing a male” and “taking a the course online” are

a. independent events;

b. dependent events;

c. mutually exclusive events;

d. none of the above

____14. Acme Airlines flies airplanes that seat 12 passengers. From experience, they have learned that, on average, 80% of the passengers holding reservations for a particular flight actually show up for the flight. If they book 13 passengers for a flight, what is the probability that 12 or fewer passengers holding reservations will actually show up for the flight? (HINT: Find complement, probability that 13 show up and subtract from 1)

a. less than 90% b. between 90 and 95%, inclusive

c. more than 95% d. cannot be determined from

____15. What is the minimum percentage of data in any frequency distribution that lies within 3 standard deviations of its mean?

a. 67% b. 75%

c. 25% d. answer not listed.

____16. Let X be a normally distributed random variable with u=100 and o=10 (SD) . The probability that X is between 70 and 110 is (to the nearest whole percent)

a. 8 % b. 84 % c. 95% d. answer not listed

____17. If events A and B are complementary events, each with non-zero

probability, then

a. A and B are mutually exclusive

b. A and B are independent

c. both (a) and (b)

d. neither (a) nor (b)

____18. If A and B are independent events then

a. P(A or B) = P(A) + P(B)

b. P(A and B) = P(A) *P(B)

c. both (a) and (b)

d. neither (a) nor (b)

_____19. In selecting a sample from a population for the purpose of making an inference from the sample about the population, it is important

a. that the sample be chosen randomly

b. that the sample have a minimum size of n = 10

c. both (a) and (b)

d. neither (a) nor (b)

_____20. If all possible random samples of size n are selected from a population with mean U and standard deviation O, then the following is true:

a. Ux = Ux/n

b. Ox = O/√n

c. Ux = Ux/√n

d. Ox = O/n

_____ 21. Let a random sample be taken of size n=100 from a population with known standard deviation of O=20 . Suppose that the mean of the sample is X=37 . The approximate 95% confidence interval for the mean, U , of the population from which the sample was drawn is (HINT: Solve using confidence interval estimate of the population Mean U with O known or you can assume the data is bell-shaped and Apply the Empirical Rule).

a. 9 ≤ U ≤ 65

b. 33 ≤ U ≤ 41

c. 35 ≤ U ≤ 39

d. -3 ≤ U ≤ 77

_____ 22. Among 100 people randomly chosen in a survey, exactly 10 stated that they believed that the elected representatives are honest most of the time. The approximate 99% confidence interval for the percentage of

the population who believe that such people are honest most of the time is

a. .02 ≤ p ≤ .18

b. .04 ≤ p ≤ .16

c. .8 ≤ p ≤ 1.2

d. 0.16 ≤ p ≤ .40

______23. Let X be a random variable representing the sum of n trials.

Then X is a binomial random variable if all of the following are

satisfied except

a. the number of trials is finite

b. p , the probability of "success" is different for all trails

c. each trial has exactly two possible outcomes

d. the trials are independent

______ 24. Each of the following is a measure of center except

a. the mean

b. the median

c. the standard deviation

d. the mode

______ 25. A sample is necessarily random if

a. the sample is chosen without replacement from the population

b. the sample is chosen with replacement from the population

c. each member of the population had an equally likely chance of being

chosen for the sample

d. none of the above

-1, 0, 2, 3, 7, 10, 10

_____1. The mean, X , of the data above is (to the nearest 1/10)

a. 8.3 b. 9.0 c. 9.4 d. 4.4

_____2. The median of the data above is

a. 5 b. 7 c. 10 d. 3

_____3. The mode of the data above is

a. 8.3 b. 10 c. 5 d. 7

_____4. The standard deviation of the data above is (to the nearest 1/10)

a. 5.0 b. 5.3 c. 6.3 d. 4.6

The table below shows the frequency distribution for 10 students on a test with a maximum score of 12. Use these sample data to answer questions 5 through 7:

Score Frequency

1-3 4

4-6 3

7-9 2

10-12 1

______5. The mean score, X , of the data in the frequency distribution above is (to the nearest 1/10)

a. 5.0 b. 5.3 c. 5.4 d. answer not listed

______6. The standard deviation of the scores in the frequency distribution above is (to the nearest 1/10)

a. 1.8 b. 3.0 c. 3.2 d. answer not listed

_____7. The median score lies in which score interval?

a. 1 – 3 b. 4 – 6 c. 7 - 9 d. 10 - 12

_____8. A delivery truck must make stops in eight different cities, designated by the first letter in the name of the city: A, B, C, D, E, F, G, and H. If the order in which the truck visits the eight locations is chosen randomly, what is the probability that it will visit them in alphabetical order? (HINT: Let A = number of ways the truck can visit the eight locations in alphabetical order and B = total number of ways the truck can visit the eight locations, find A/B)

a. 8C1/8P1

b. 1/8P8

c. 1/8C8

d. answer not listed

_____9. A jar contains 12 marbles, 5 of which are blue and 7 of which are red. If 4 marbles are chosen at random and without replacement, what is the probability of selecting 3 blue ones and 1 red one? (HINT: First, Determine how many ways to select 3 blue marbles AND 1 red marble. Then, determine how many total ways to select 4 marbles)

a. (5C3 * 7C1) / 12C4

b. (5P3 * 7P1) / 12P4

c. (5C2 * 7P2) / 12

d. answer not listed

_____10. Suppose that P(A| B) = P(A) , P(Aand B)=.36 , and P(A)=.9 . What is P(B) ? (HINT: Use Formal Multiplication Rule and Intuitive Multiplication Rule)

a. 0.004 b. 0.04 c. 0.4 d. answer not listed

For questions 11 through 13 use the table immediately below. The table shows the number of students who are taking a statistics course in the traditional face-to-face mode versus online by sex. Assume one person is chosen at random from the 220.

Online Traditional Totals

Male 30 60 90

Female 40 90 130

Totals 70 150 220

_____11. If a student taking the course online is chosen at random, the probability that the person is male is

a. 3/22 b. 9/22 c. 1/3 d. 3/7

_____12. If a male is chosen at random, the probability that he is taking the course in the traditional mode is

a. 7/22 b. 2/3 c. 2/5 d. answer not listed

_____13. The events of “choosing a male” and “taking a the course online” are

a. independent events;

b. dependent events;

c. mutually exclusive events;

d. none of the above

____14. Acme Airlines flies airplanes that seat 12 passengers. From experience, they have learned that, on average, 80% of the passengers holding reservations for a particular flight actually show up for the flight. If they book 13 passengers for a flight, what is the probability that 12 or fewer passengers holding reservations will actually show up for the flight? (HINT: Find complement, probability that 13 show up and subtract from 1)

a. less than 90% b. between 90 and 95%, inclusive

c. more than 95% d. cannot be determined from

____15. What is the minimum percentage of data in any frequency distribution that lies within 3 standard deviations of its mean?

a. 67% b. 75%

c. 25% d. answer not listed.

____16. Let X be a normally distributed random variable with u=100 and o=10 (SD) . The probability that X is between 70 and 110 is (to the nearest whole percent)

a. 8 % b. 84 % c. 95% d. answer not listed

____17. If events A and B are complementary events, each with non-zero

probability, then

a. A and B are mutually exclusive

b. A and B are independent

c. both (a) and (b)

d. neither (a) nor (b)

____18. If A and B are independent events then

a. P(A or B) = P(A) + P(B)

b. P(A and B) = P(A) *P(B)

c. both (a) and (b)

d. neither (a) nor (b)

_____19. In selecting a sample from a population for the purpose of making an inference from the sample about the population, it is important

a. that the sample be chosen randomly

b. that the sample have a minimum size of n = 10

c. both (a) and (b)

d. neither (a) nor (b)

_____20. If all possible random samples of size n are selected from a population with mean U and standard deviation O, then the following is true:

a. Ux = Ux/n

b. Ox = O/√n

c. Ux = Ux/√n

d. Ox = O/n

_____ 21. Let a random sample be taken of size n=100 from a population with known standard deviation of O=20 . Suppose that the mean of the sample is X=37 . The approximate 95% confidence interval for the mean, U , of the population from which the sample was drawn is (HINT: Solve using confidence interval estimate of the population Mean U with O known or you can assume the data is bell-shaped and Apply the Empirical Rule).

a. 9 ≤ U ≤ 65

b. 33 ≤ U ≤ 41

c. 35 ≤ U ≤ 39

d. -3 ≤ U ≤ 77

_____ 22. Among 100 people randomly chosen in a survey, exactly 10 stated that they believed that the elected representatives are honest most of the time. The approximate 99% confidence interval for the percentage of

the population who believe that such people are honest most of the time is

a. .02 ≤ p ≤ .18

b. .04 ≤ p ≤ .16

c. .8 ≤ p ≤ 1.2

d. 0.16 ≤ p ≤ .40

______23. Let X be a random variable representing the sum of n trials.

Then X is a binomial random variable if all of the following are

satisfied except

a. the number of trials is finite

b. p , the probability of "success" is different for all trails

c. each trial has exactly two possible outcomes

d. the trials are independent

______ 24. Each of the following is a measure of center except

a. the mean

b. the median

c. the standard deviation

d. the mode

______ 25. A sample is necessarily random if

a. the sample is chosen without replacement from the population

b. the sample is chosen with replacement from the population

c. each member of the population had an equally likely chance of being

chosen for the sample

d. none of the above

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