ST 370 Final

C. Independent

In a Binomial Probability Distribution, each trial is __________of every other trial. a. contingent b. dependent c. independent d. both dependent and independent

C) 0.090

In one town, 30% of all voters are Democrats. If two voters are randomly selected for a survey, find the probability that they are both Democrats. A) 0.300 B) 0.087 C) 0.090 D) 0.600

c. Yes, because each adult has a 70% chance.

Approximately 70% of U.S. adults had at least one pet as a child. We randomly survey 60 U. S. adults. We are interested in the number that had at least one pet as a child. Does X follow a Binomial Distribution? a. No, because not all children can have pets. b. No, because 30% did not have pets. c. Yes, because each adult has a 70% chance. d. Yes, because most children like pets.

d. P(X=3)+P(X=4)+P(X=5)+ ...

Approximately 70% of U.S. adults had at least one pet as a child. We randomly survey 60 U. S. adults. We are interested in the number that had at least one pet as a child. The probability that at least 3 adults had at least one pet as a child means: a. P(X=0)+P(X=1)+P(X=2)+P(X=3) b. P(X=0)+P(X=1)+P(X=2) c. P(X=4)+P(X=5)+P(X=6)+ ... d. P(X=3)+P(X=4)+P(X=5)+ ...

B. 50%

Approximately what percent of the data in a sample falls between the first and third quartiles? A.) 25% B.) 50% C.) 75% D.) 95% E.) We can't be sure since we don't know whether the data is normally distributed.

D. Simple

At NCSU 10 randomly selected students are questioned to measure the college's effectiveness in achieving student learning outcomes. A. Systematic B. Judgement C. Stratified D. Simple

B. Judgement

At NCSU students entering the student center are questioned to measure the college's effectiveness in achieving student learning outcomes A. Systematic B. Judgement C. Stratified D. Simple

C. Stratified

At NCSU ten students from every class on campus are questioned to measure the colleges effectiveness in achieving student learning outcomes A. Systematic B. Judgement C. Stratified D. Simple

A) 0.685

Based on meteorological records, the probability that it will snow in a certain town on January 1st is 0.315. Find the probability that in a given year it will not snow on January 1st in that town. A) 0.685 B) 3.175 C) 0.460 D) 1.315

C. Median, Mode, Mean

Below is a histogram of the number of letters in the words that Shakespeare used in his plays. Where do you think the mean, median, and mode go for this histogram from left to right? iiiiiiiii iiiiiiiiiiiiii iiiiiiiiiiiiiiiiiiiiiiiiiiiii iiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii A. Mean, Median Mode B. Mode, Mean, Median C. Median, Mode, Mean D. Mode, Median, Mean E. Median, Mean, Mode

9/13

Consider the experiment of selecting a card from an ordinary deck of 52 playing cards. A card is drawn is neither a king nor a spade

3/26

Consider the experiment of selecting a card from an ordinary deck of 52 playing cards. A card that is a black face card is drawn.

10/13

Consider the experiment of selecting a card from an ordinary deck of 52 playing cards. A card that is not a face card is drawn.

12/52

Consider the experiment of selecting a card from an ordinary deck of 52 playing cards. A face card is drawn

10/13

Consider the experiment of selecting a card from an ordinary deck of 52 playing cards. A non-face card or a 7 is drawn

7/13

Consider the experiment of selecting a card from an ordinary deck of 52 playing cards. A red card or a card showing a 5 is drawn

Valid probability distribution

Determine whether the following is a probability distribution. If not, identify the requirement that is not satisfied. x P(x) 1, .18 2, .19 3, .13 4, .47 5, .03

Not a probability distribution since probability is not equal to 1

Determine whether the following is a probability distribution. If not, identify the requirement that is not satisfied. x P(x) 1, .0370 2, .2 3, .444 4, .2960

Complementary Events

Difference between sample space and subset of sample space is considered as: A. numerical complementary events B. Equal Compulsory events C. Complementary Events D. Compulsory Events

B) Yes

Draw one ball colored red from a bag. (Assuming the bag has red or blue colors) Draw one ball colored blue from the same bag. A) No B) Yes

c. 41/54

11. There is a 13/54 probability that the card chosen is a spade, a 13/54 probability that the card is a heart, a 13/54 probability that the card is a diamond, and a 13/54 probability that the card is a club. Both spades and clubs are black cards, while hearts and diamonds are red. In addition, one of the jokers is a black card and the other joker, a red card. The probability that the card chosen is not a space is a. 13/54 b. .75 c. 41/54 d. 1.00

D) 1/3

A 6-sided die is rolled. What is the probability of rolling a 3 or a 6? A) 2 B) 1/36 C) 1/6 D) 1/3

B) 3/16

A bag contains 6 red marbles, 3 blue marbles, and 7 green marbles. If a marble is randomly selected from the bag, what is the probability that it is blue? A) 1/3 B) 3/16 C) 1/13 D) 1/7

A. .1

A bag contains nickels, dimes, and quarters (more than two of each). Two coins are randomly selected and their total value in cents is noted. Find the possible values of the random variable X. Using the table, find the missing value. x p(x) 0, .1 1, .2 2, x 4, .3 6, .3 A. .1 B. .7 C. .3 D. .6

b. 0.91.

A basketball player makes 70% of her free throws. When fouled, she gets to take 2 free throws. Let X represent the number of free throws made in two tries. The probability distribution for the number of free throws she makes in two attempts is summarized in the following table: F P(F) 0, .09 1, .42 2, .49 The probability that she makes at least one free throw is a. 0.67. b. 0.91. c. 0.95. d. 1.00.

a. P(X ≥ 1).

A basketball player makes 70% of her free throws. When fouled, she gets to take 2 free throws. Let X represent the number of free throws made in two tries. The probability distribution for the number of free throws she makes in two attempts is summarized in the following table: F P(F) 0, .09 1, .42 2, .49 The probability that she makes at least one free throw is expressed as a. P(X ≥ 1). b. P(X ≤ 1). c. P(X < 1). d. P(X > 1).

C) {7, 8, 9, 10, 11, 12, 13}

A box contains 13 white cards numbered 1 through 13. List the outcomes of the event the card drawn has a number greater than 6. Circle the best answer. A) {1, 2, 3, ... 13} B) {11} C) {7, 8, 9, 10, 11, 12, 13} D) {6, 7, 8, 9, 10, 11, 12, 13}

S = {1, 2, 3, ... 13}

A box contains 13 white cards numbered 1 through 13. List the sample space associated with drawing a single card and noting the number printed on it.

C) 5/6

A die with 12 sides is rolled. What is the probability of rolling a number less than 11? A) 1/12 B) 10 C) 5/6 D) 11/12

b. .368

According to the October 2003 Current Population Survey, the following table summarizes probabilities for randomly selecting a full-time student in various age groups: Age P(x) 15-17, .009 18-24, .623 25-34, .210 35+, .158 If we randomly select a full-time student, what is the probability that he/she is 25 or older? a. .250 b. .368 c. .623 d. impossible to determine from the information given.

A.) Standard deviation is a measure of the average distance of the observations from their mean.

20. Which of the following is true about standard deviation? A.) Standard deviation is a measure of the average distance of the observations from their mean. B.) Standard deviation is the squared average distance between the observations. C.) Standard deviation is the measure of the relationship between X and Y. D.) If the mean of a random variable is 0, then its standard deviation is 0 as well. E.) Two of the above are true.

C. Mode

21. The following set of data represents letter grades on term papers in a rhetoric class: A, A, A, B, B, B, B, C, C, C, C, C, C, C, C, C, C, C, D, D, D, F. Select the most appropriate measure of central tendency for the data described. A. Mean B. Median C. Mode D. Midrange

??

22. Adding 5 to each value in a data set would not change which of the following measures? A. Mode B. Mean C. Mid-range D. Standard deviation

A) 0.343

A manufacturing process has a 70% yield, meaning that 70% of the products are acceptable and 30% are defective. If three of the products are randomly selected, find the probability that all of them are acceptable. A) 0.343 B) 0.027 C) 0.429 D) 2.1

B.) 1.5*IQR above Q3

A member of a data set would be an outlier if it falls more than A.) 1.5*IQR above Q1 B.) 1.5*IQR above Q3 C.) 1.5*IQR above the median D.) 1.5*IQR above the mean E.) All of the above choices describe an outlier.

A) No

A multiple choice question has 14 possible answers, only one of which is correct. Is it "unusual" to answer a question correctly if a random guess is made? A) No B) Yes

B. Discrete

A pair of dice is rolled, the sum is recorded A. Continuous B. Discrete

C. .6

A polling firm, hired to estimate the likelihood of the passage of an upcoming referendum, obtained the set of survey responses to make its estimate. The encoding system for the data is: 1 = FOR, 2 = AGAINST. If the referendum were held today, estimate the probability that it would pass. 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1 A. .5 B. .65 C. .6 D. .4

C) 0.1491

A sample of 4 different calculators is randomly selected from a group containing 36 that are defective and 21 that have no defects. What is the probability that all four of the calculators selected are defective? A) 9.8421 B) 0.1158 C) 0.1491 D) 0.1591

C) 1/80

A sample space consists of 80 simple events that are equally likely. What is the probability of each? A) 1 B) 0 C) 1/80 D) 80

A. 2/3

A spinner has equal regions numbered 1 through 15. What is the probability that the spinner will stop on an even number or a multiple of 3? A. 2/3 B. 1/3 C. 12 D. 7/9

B) Dependent

A: A Chicagoan visits New York on vacation. B: He visits Central Park. A) Independent B) Dependent

A) Dependent

A: A green ball is drawn from a box with five balls and placed next to the box. B: A red ball is drawn next and placed next to the green one. A) Dependent B) Independent

B) Dependent

A: A mosquito lands on your arm. B: You get a mosquito bite. A) Independent B) Dependent

d. impossible to determine from the information provided.

According to the October 2003 Current Population Survey, the following table summarizes probabilities for randomly selecting a full-time student in various age groups: Age P(x) 15-17, .009 18-24, .623 25-34, .210 35+, .158 If we randomly select a full-time student, the probability that he/she is 18-30 years old is a. .50. b. .623. c. .842. d. impossible to determine from the information provided.

a. .377

According to the October 2003 Current Population Survey, the following table summarizes probabilities for randomly selecting a full-time student in various age groups: Age P(x) 15-17, .009 18-24, .623 25-34, .210 35+, .158 If we randomly select a full-time student, the probability that he/she is not 18-24 years old is a. .377. b. .623. c. .75. d. 1.

B) 0.413

Find P( ), given that P(A) = 0.587. A) 1.704 B) 0.413 C) 0 D) 1.587

A) No

Find a ten dollar bill on the sidewalk. Find a ten dollar bill on the grass. A) No B) Yes

k = .11

Find all values of K so that the following is a probability distribution X P(x) 1, .15 2, .2k 3, .52 4, k

C) 1/216

Find the probability of correctly answering the first 3 questions on a multiple choice test if random guesses are made and each question has 6 possible answers. A) 2 B) 1/2 C) 1/216 D) 1/729

Sample Space

For a random experiment, all possible outcomes are called: a. numerical space b. event space c. sample space d. both b and c

a. .35

Given: P(A) = .4 P(B) = .6 P(A or B) = .65 Find P(A and B) a. .35 b. 1 c. 05 d. .24

A. Quantitative

High temperatures in C are recorded daily at a weather station A. Quantitative B. Qualitative

A) 7/19

If P(A) = 12/19, find P( ). A) 7/19 B) 12/31 C) 0 D) 19/12

d. P(J or K) =.72

If P(J) = 0.3, P(K) = 0.6, and J and K are independent events, then: a. P(J and K) = 0 b. P(J or K) = 0 c. P(J) does not equal P(J|K) d. P(J or K) =.72

C) 334/365

If a person is randomly selected, find the probability that his or her birthday is not in May. Ignore leap years. A) 31/334 B) 31/365 C) 334/365 D) 11/12

A) Yes

Is it "unusual" to get a sum of the outcome is 12 when a pair of dice is rolled? A) Yes B) No

A) No

Is it "unusual" to get a sum of the outcome is 3 when a pair of dice is rolled? A) No B) Yes

d. 0.95

Management for a chain of restaurants recorded the number of appetizers, X, ordered by tables dining. They observed that X had the following probability distribution. X P(x) 0, .60 1, .35 2, .04 3+, .01 21. What is P(X < 2)? a. 0.04 b. 0.35 c. 0.60 d. 0.95

b. 0.39

Management for a chain of restaurants recorded the number of appetizers, X, ordered by tables dining. They observed that X had the following probability distribution. X P(x) 0, .60 1, .35 2, .04 3+, .01 The probability that a randomly chosen table orders at least one appetizer is a. 0.35. b. 0.39. c. 0.40. d. none of the above.

B) No

Meet a man with an umbrella. Meet a man with a raincoat. A) Yes B) No

c. 0, 1, 2, ..., 14

Ninety-four percent of NCSU transfers feel that their college adequately prepared them to handle upper-division coursework at their transfer university. We randomly survey 14 NCSU transfers. We are interested in the number that feel that their college adequately prepared them to handle upper division coursework at their transfer university. List the values that X, the Random Variable, may take on. a. 0, 1, 2, ..., 94 b. 1, 2, 3, ..., 14 c. 0, 1, 2, ..., 14 d. 1, 2, 3, ..., 94

4

Number of sample points for an experiment in which two coins are tossed

A. Median and IRQ

Of the following, which combination is the BEST choice for describing the center and spread of a RIGHT-SKEWED distribution? A.) median and IQR B.) mean and standard deviation C.) mean and variance D.) mode and IQR E.) median and standard deviation

C) 1/4

On a multiple choice test, each question has 4 possible answers. If you make a random guess on the first question, what is the probability that you are correct? A) 4 B) 1 C) 1/4 D) 0

B. Sample

One hundred statistics students are gathered to measure IQ levels A. Population B. Sample

B. Discrete

Out of 1 0 times connecting to an internet provider, the average number of attempts before connecting A. Continuous B. Discrete

B. Qualitative

Phone numbers are gathered from all NCSU students A. Quantitative B. Qualitative

B. HH HT TH TT

Sample Space Flip coin Twice

D. HHH HHT HTH HTT THH THT TTH TTT

Sample Space Flip coin three times

A. Systematic

Students are selected by selecting names corresponding to every 50th students ID A. Systematic B. Judgement C. Stratified D. Simple

A. Population

The age of all NCSU Students are collected A. Population B. Sample

A. Statistic

The average IQ of one hundred students is computed A. Statistic B. Parameter

B. Parameter

The average age of all NCSU students is computed A. Statistic B. Parameter

A. Continuous

The cost of an orange A. Continuous B. Discrete

B. .7

The data set represents the income levels of the members of a country club. Estimate the probability that a randomly selected member earns at least $91,000. 103,000 115,000 87,000 121,000 89,000 103,000 91,000 83,000 133,000 163,000 85,000 97,000 127,000 89,000 115,000 109,000 91,000 139,000 81,000 109,000 A. .4 B. .7 C. .8 D. .6

D. .682

The distribution of BA degrees is the following: English 2073 Math 2164 Chem 318 Physics 856 Liberal Arts 1358 Business 1676 Engineering 868 Total 9313 What is the probability that a randomly selected student is not math? A. .232 B. .768 C. .303 D. .682

C. 20

The following is a sample of the ages of students in a typical NCSU class: 18 20 21 18 19 20 20 21 19 The mode for the above sample is: A. 18 B. 19 C. 20 D. 21

C. 20

The following is a sample of the ages of students in a typical NCSU class: 18 20 21 18 19 20 20 21 19 The median for the sample is: A. 18 B. 19 C. 20 D. 21

B. Continuous

The heights of randomly selected trees are measured by the forest service A. Discrete B. Continuous

A. Nominal

The names of various tree species are gathered and recorded A. Nominal B. Ordinal

A. Discrete

The number of oil spills occurring off of the Alaskan coast A. Continuous B. Discrete

B. Discrete

The number of phone calls between NY and California A. Continuous B. Discrete

B. Discrete

The number of times required for a modem to dial an internet provider before connecting A. Continuous B. Discrete

A. Discrete

The number of trees in each acre of a forest is monitored by the forest service A. Discrete B. Continuous

A. Continuous

The pH level in a bottle of shampoo A. Continuous B. Discrete

D) 0.01

The probability that Luis will pass his statistics test is 0.99. Find the probability that he will fail his statistics test. A) 0.50 B) 99.00 C) 1.01 D) 0.01

B. Ordinal

The states of health for randomly selected tree are classified as "poor" or "good" or "very good" A. Nominal B. Ordinal

A. Continuous

The weight of bags with 10 apples in each A. Continuous B. Discrete

C. 1/27

There is a 13/54 probability that the card chosen is a spade, a 13/54 probability that the card is a heart, a 13/54 probability that the card is a diamond, and a 13/54 probability that the card is a club. Both spades and clubs are black cards, while hearts and diamonds are red. In addition, one of the jokers is a black card and the other joker, a red card. The probability that the card chosen is a joker is? a. 1/2 b. 1/13 c. 1/27 d. 41/54

B. .50

There is a 13/54 probability that the card chosen is a spade, a 13/54 probability that the card is a heart, a 13/54 probability that the card is a diamond, and a 13/54 probability that the card is a club. Both spades and clubs are black cards, while hearts and diamonds are red. In addition, one of the jokers is a black card and the other joker, a red card. What is the probability that the card chosen is red? a. .25 b. .50 c. .75 d. 1.00

B. Number of attempts to make a field goal in football.

Which of the following would not be a continuous random variable? A. Age of student upon graduation from college. B. Number of attempts to make a field goal in football. C. Number of miles driven on a trip. D. Body temperature of small children.

d. dependent on the first pick

When sampling is done without replacement, the second pick is: a. independent from the first pick b. a complement of the first pick c. mutually exclusive from the first pick d. dependent on the first pick

C. P(x) = 1/3 x = 3,4,5

Which of the following is a valid probability distribution? A. P(x) = 1/2 x= 1,2,3 B. P(x) = x^2 /2 x = -1, 1, 2 C. P(x) = 1/3 x = 3,4,5 D. P(x) = -x/2 x=-1,0,1

D None of the above

Which of the following is an example of binomial experiment? (a) A survey on customer income at a shopping mall (b) Weight gains in beef cattle under two different types of feed (c) A study of the average number of hours worked by high school student (d) None of the above

A. Pie chart

Which of the following is not appropriate for quantitative data? a. Pie chart b. Histogram c. Box Plots d. Stem + Leaf e. All of them

D. Mean

Which of the following is not the same as the other answers? A. Median B. Fiftieth Percentile C. Second Quartile D. Mean

B. Observing the number of light bulbs burned out on a display sign

Which of the following probability experiments would result in a discrete random variable? A. Observing the number of minutes required to walk a mile B. Observing the number of light bulbs burned out on a display sign C. Observing the number of inches tall of second grade students D. Observing the number of pounds in each of 15 bags of apples

d. 4/36.

You roll a pair of fair dice and compute the number of spots on the two sides facing up. Denote this total by X. The probability distribution of X is X P(x) 2, 1/36 3, 2/36 4, 3/36 5, 4/36 6, 6/36 7, 6/36 8, 5/36 9, 4/36 10, 3/36 11, 2/36 12,1/36 The probability that X is a 2, 11, or 12 is a. 1/36. b. 2/36 c. 3/36. d. 4/36.

d. 21/36.

You roll a pair of fair dice and compute the number of spots on the two sides facing up. Denote this total by X. The probability distribution of X is X P(x) 2, 1/36 3, 2/36 4, 3/36 5, 4/36 6, 6/36 7, 6/36 8, 5/36 9, 4/36 10, 3/36 11, 2/36 12,1/36 The probability that X is at least 7 is a. 5/36. b. 6/36. c. 15/36. d. 21/36.