Stats Semester Exam Review

94. let the random variable x represent the profit made on a randomly selected day by a certain store. assume x is normal with a mean of $360 and standard deviation $50. the value of p(x>$400) is

.2119

81. a student is chosen at random from the river city high school student body, and the following events are recorded: m= the student is male f= the student is female b= the student ate breakfast that morning n= the student did not eat breakfast that morning the following diagram gives probabilities associated with these events. find p(b given f) and write in words what this expression represents.

.3, the probability the student ate breakfast, given she is female

27. a company produces ceramic floor tiles that are supposed to have a surface area of 16.0 square inches. due to variability in the manufacturing process, the actual surface area has a normal distribution with a mean of 16.1 square inches and a standard deviation of 0.2 square inches. the proportion of tiles produced by the process with surface area less than 16.0 square inches is

.3085

76. event a occurs with probability 0.8. the conditional probability that event b occurs, given that a occurs, is 0.5. the probability that both a and b occurs is

.4

79. a student is chosen at random from the river city high school student body, and the following events are recorded: m= the student is male f= the student is female b= the student ate breakfast that morning n= the student did not eat breakfast that morning the following diagram gives probabilities associated with these events. what is the probability that the student had breakfast?

.5

72. suppose that a and b are independent events with p(a)=0.2 and p(b)=0.4. p(a and b) is

.52

85. one hundred high school students were asked if they had a dog, a cat, or both at home. here are the results... if two students are selected at random, what is the probability that neither of them has a dog or a cat?

.548

36. consider the following scatterplot, which describes the relationship between stopping distance (in feet) and air temperature (in degrees centigrade) for a certain 2000-pound car travelling 40 mph. the correlation between temperature and stopping distance is

.6

80. a student is chosen at random from the river city high school student body, and the following events are recorded: m= the student is male f= the student is female b= the student ate breakfast that morning n= the student did not eat breakfast that morning the following diagram gives probabilities associated with these events. given that the student who ate breakfast is selected, what is the probability that he is male?

.64

84. one hundred high school students were asked if they had a dog, a cat, or both at home. here are the results... if a single student is selected at random and you know she has a dog, what is the probability she also has a cat?

.75

69. ignoring twins and other multiple births, assume that babies born at a hospital are independent random events with the probability that a baby is a boy and the probability that a baby is a girl both equal to 0.5. the probability that at least one of the next three babies is a boy is

.875

88. flip a coin four times. if z= the number of heads in four flips, then the probability distribution of z is given in the table below... the probability of at least one tail is

.9375

67. event a has probability 0.4. event b has probability 0.5. if a and b are disjoint, then the probability that both events occur is

0.0

1. you measure the age, marital status and earned income of an SRS of 1463 women. the number and type of variables you have measured is

3, 1 categorical and 2 quantitative

16. here is a list of exam scores for the 14 students in mr. williams' calculus class. what is the percentile of the person whose score was 85?

71

29. you are chatting with the principal of a local high school. the topic of sat scores comes up, and the principal mentions that sat scores at the school are normally distributed. she doesn't remember the mean or the standard deviation, but she does remember that the upper and lower quartiles are 500 and 600. the standard deviation of dat verbal scores is closest to

75 points

12. a lobster fisherman is keeping track of the productivity of a set of traps he has placed in a favorite location. below are the numbers of lobsters in these traps over the course of 12 different hauls. according to the 1.5 x iqr rule, which values in the above distribution are outliers?

14

7. mr. williams asked the 26 seniors in his statistics class how many ap courses they had taken during high school. below is a dot plot summarizing the results of his survey. which of the following is a correct dot plot for these data?

B- the one with no line in the middle :(

52. you want to know the opinions of american school teachers about establishing a national test for high school graduation. you obtain a list of the members of the national education association (the largest teachers' union) and mail a questionnaire to 2500 teachers chosen at random from this list. in all 1347 teachers return the questionnaire. the population is

all american schoolteachers

93. the density curve for a continuous random variable x has which of the following properties? the probability of any event is the area under the density curve between the values of x that make up the event. the total area under the density curve for x must be exactly 1. p(x=a)=0 for any constant a . the density curve lies completely on or above the horizontal axis

all of the above

63. frequently, telephone poll-takers call near dinner time-- between 6 pm and 7 pm-- because most people are at home then. this is an effort to avoid

nonresponse

91. in the florida scratch-card lottery, the numbers and values of prizes awarded for every 100,000 cards sold are given to the table below... the expected payoff per card is

$0.85

89. in a particular game, a fair die is tossed. if the number of spots showing is either 4 or 5 you win $1, if the number of spots showing is 6 you win $4, and if the number of spots showing is 1, 2, or 3 you win nothing. let x be the amount that you win. which of the following is the standard deviation of x?

$1.41

95. let the random variable x represent the profit made on a randomly selected day by a certain store. assume x is normal with a mean of $360 and standard deviation $50. the probability is approximately 0.6 that on a randomly selected day the store will make less than which of the following amounts?

$372.60

101. there are twenty multiple-choice questions on an exam, each having responses a, b, c, or d. each question is worth five points and only one option per question is correct. suppose the student guesses the answer to each question, and the guesses from question to question are independent. which of the following expresses the probability that the student gets no questions correct?

(.75)^20

47. below is a scatterplot (with the least-squares regression line) for calories and protein (in grams) in one cup of 11 varieties of dried beans. the computer output for this regression is below the plot. the circled point on the scatterplot represents lima beans, which have 621 calories and 37 grams of protein. the residual for lima beans is

-4.18

104. a college basketball player makes 80% of her free throws. suppose this probability is the same for each free throw she attempts, and free throw attempts are independent. the probability that she makes all of her first four free throws and then misses her fifth attempt this season is

.08192

103. the binomial expression 8C2(1/3)^2(2/3)^6 gives the probability of

.2731

105. a college basketball player makes 80% of her free throws. suppose this probability is the same for each free throw she attempts, and free throw attempts are independent. the expected number of free throws required until she makes her first free throw of the season is

1.25

102. a college basketball player makes 5/6 of his free throws. assuming free throw attempts are independent, the probability that he makes exactly three of his next four free throws is

4(1/6)^1(5/6)^3

28. the time to complete a standardized exam is approximately normal with a mean of 70 minutes and a standard deviation of 10 minutes. how much time should be given to complete the exam so that 80% of the students will complete the exam in the time given?

78.4

56. a simple random sample of size n is defined to be

a sample that gives every possible sample of the same size the same chance to be selected

44. suppose we fit the least-squares regression line to a set of data. if a plot of the residuals shows a curved pattern,

a straight line is not a good summary for the data

54. a television station is interested in predicting whether voters in its viewing area are in favor of offshore drilling. it asks its viewers to phone in and indicate whether they support/are in favor of or are opposed to this practice. of the 2241 viewers who phoned in, 1574 (70%) were opposed to offshore drilling. the viewers who phoned in are

a voluntary response sample

65. the essential difference between an experiment and an observational study is that

an experiment imposes treatments on the subjects, but an observational study does not

2. the table below shows the results of the new hampshire republican presidential primary on january 10, 2012. which of the following graphs are all appropriate ways of presenting these data?

bar graph, pie chart

64. which of the following is not a major principle of good design for all experiments?

blocking

37. consider the following scatterplot, which describes the relationship between stopping distance (in feet) and air temperature (in degrees centigrade) for a certain 2000-pound car travelling 40 mph. if another data point were added with an air temperature of 0 degrees C and a stopping distance of 80 feet, the correlation would

decrease, since this new point is an outlier that does not follow the pattern in the data

18. a standard score describes

how far a particular score is from the mean

6. a random sample of 100 students in grades 10 through 12 were sampled and asked their year in school and whether they were involved in interscholastic sports, intramural sports, or no sports. the results are summarized in the segmented bar graph below. based on this graph, which of the following statements is true?

juniors have the highest percentage participation in intramurals

34. two variables are said to be negatively associated if

large values of one variable are associated with small values of the other

75. suppose we roll two six-sided dice-- one red and one green. let a be the event that the number of spots showing on the red die is three or less and b be the event that the number of spots showing on the green die is three or more. the event corresponding to the system failing during one period of operation is

look back at this one

20. a data set is normally distributed with a mean of 25 and a standard deviation of 8. if you calculate the standard score of every observation in this data set, what will the mean and standard deviation of the resulting scores be?

mean=0, standard deviation=1

4. the histogram below shows the distribution of heights for 100 randomly selected school children in great britain. which of the following descriptions best fits this distribution?

roughly symmetric with center 150 and range 80

21. if 30 is added to every number on a list, which one of the following does not change?

standard deviation

32. the height (in feet) and volume (in cubic feet) of usable lumber of 32 cherry trees are measured by a researcher. the goal is to determine if volume of usable lumber can be estimated from the height of a tree. in the study, the response variable is

volume of lumber

15. you are told that your score on an exam is at the 85 percentile of the distribution of scores. which of the following is a correct interpretation of this information?

your score was higher than approximately 85% of the people who took this exam

25. birth weights at a local hospital a normal distribution with a mean of 110 oz and a standard deviation of 15 oz. which of the following is the proportion of infants with birth weights between 125 oz and 140 oz?

.1359

68. ignoring twins and other multiple births, assume that babies born at a hospital are independent random events with the probability that a baby is a boy and the probability that a baby is a girl both equal to 0.5. the probability that the next five babies are girls is

.03125

90. in the florida scratch-card lottery, the numbers and values of prizes awarded for every 100,000 cards sold are given to the table below... the probability that a random scratch-card will pay off is

.0601

39. consider the following scatterplot of the amounts of co (carbon monoxide) and nox (nitrogen oxide) in grams per mile driven in the exhaust of cars. the least-squares regression line has been drawn in the plot. based on the scatterplot, the least-squares line would predict that a car that emits 10 grams of co per mile driven would emit approximately how many grams of nox per mile driven?

1.1

38. consider the following scatterplot of the amounts of co (carbon monoxide) and nox (nitrogen oxide) in grams per mile driven in the exhaust of cars. the least-squares regression line has been drawn in the plot. the intercept of the least-squares regression line is approximately

1.8

86. one hundred high school students were asked if they had a dog, a cat, or both at home. here are the results... let x be the outcome of rolling a fair six-sided die. p(2<=x<5)=

1/2

78. the card game euchre uses a deck with 32 cards: ace, king, queen, jack, 10, 9, 8, 7 of each suit. suppose you choose one card at random from a well-shuffled euchre deck. what is the probability that the card is a jack, given that you know it's a face card?

1/3

73. in a particular game, a fair die is tossed. if the number of spots showing is either four or five, you score 1 point. if the number of spots showing is six, you score 4 points. and if the number of spots showing is one, two, or three, you score 0. you are going to play the game twice. the probability that you score 4 points both times is

1/36

9. the following is a boxplot of the birth weights (in ounces) of a sample of 160 infants born in a local hospital. about 40 of the birth weights were below

102 ounces

96. your friend albert has invented a game involving two ten-sided dice. one of the dice has threes, fours, and fives on its faces, the other has sixes, eights, and tens. he won't tell you how many of each number there are on the faces, but he does tell you that if x= the result of a single roll of the first die and y= the result of a single roll of the second die, then meanx=3.6, sdx=0.8, meany=8.0, sdy=0.9. let z= the sum of the dice when each is rolled once. what is the expected value of z?

11.6

8. the following is a boxplot of the birth weights (in ounces) of a sample of 160 infants born in a local hospital. the median birth weight is approximately

110 ounces

51. a fisheries biologist studying whitefish in a canadian lake collected data on the length (in centimeters) and egg production for 25 female fish. a scatterplot of her results and computer regression analysis of egg production versus fish length are given below. on average, how far are the predicted y-values from the actual y-values?

25.55

92. a small store keeps track of customers that make a purchase during the first hour that the store is open each day. based on the records, x has the following probability distribution. use the mean number of customers that make a purchase during the first hour that the store is open.

3.0

48. below is a scatterplot (with the least-squares regression line) for calories and protein (in grams) in one cup of 11 varieties of dried beans. the computer output for this regression is below the plot. if we were to use this least-squares regression line to predict the protein content of another bean variety on the basis of calorie content, which of the following values from the computer output describes the expected average error in our prediction?

3.37648

71. in a certain town, 60% of the households have fiber optic internet access, 30% have at least one high-definition television, and 20% have both. the proportion of households that have neither fiber optic internet or high-definition television is

30%

30. entomologist heinz kaefer has a colony of bongo spiders in his lab. there are 1000 adult spiders in the colony, and their weights are normally distributed with mean 11 grams and standard deviation 2 grams. about how many spiders are there in the colony which weigh more than 12 grams?

308.5 spiders

98. the mp3 music files on sharon's computer have a mean size of 4.0 megabytes and a standard deviation of 1.8 megabytes. she wants to create a mix of 10 of the songs for a friend. let the random variable t= the total size (in megabytes) for 10 randomly selected songs from sharon's computer. what is the expected value of t?

40.0

58. you want to take an srs of 50 of the 816 students who live in a dormitory on campus. you label the students 001 to 816 in alphabetical order. in the table of random digits you read the entries 95592 94007 69769 33547 72450 16632 81194 14873. the first three students in your sample have labels

400, 769, 335

26. iqs among undergraduates at mountain tech are approximately normally distributed. the mean undergraduate iq is 110. about 95% of undergraduates have iqs between 100 and 120. the standard deviation of these iqs is about

5

74. suppose we roll two six-sided dice-- one red and one green. let a be the event that the number of spots showing on the red die is three or less and b be the event that the number of spots showing on the green die is three or more. p(a or b)=

5/6

10. the following is a boxplot of the birth weights (in ounces) of a sample of 160 infants born in a local hospital. the number of children with birth weights between 102 and 122 ounces is approximately

80 children

59. you want to take an srs of 50 of the 816 students who live in a dormitory on campus. you label the students 001 to 816 in alphabetical order. in the table of random digits you read the entries 95592 94007 69769 33547 72450 16632 81194 14873. another choice of labels for the 816 students is

b&c b- still 001 to 816, but in order of the students' id numbers c- 000 to 815 in alphabetical order

22. a sample was taken of the salaries of 20 employees of a large company. the following are the salaries (in thousands of dollars) for this year. For convenience, the data are ordered. suppose each employee receives a $3000 raise for next year (each employee's salary is increased by $3000). the standard deviation of the salaries for the employees will

be unchanged

23. a sample was taken of the salaries of 20 employees of a large company. the following are the salaries (in thousands of dollars) for this year. For convenience, the data are ordered. suppose each employee receives a $3000 raise for next year (each employee's salary is increased by $3000). the iqr of the salaries for the employees will

be unchanged

24. a sample was taken of the salaries of 20 employees of a large company. the following are the salaries (in thousands of dollars) for this year. For convenience, the data are ordered. suppose each employee receives a $3000 raise for next year (each employee's salary is increased by $3000). the z-scores of the salaries for the employees will

be unchanged

55. a news release for a diet products company reports: "there's good news for the 65 million americans currently on a diet." its study showed that people who lose weight can keep it off. the sample was twenty graduates of the company's program who endorse it in commercials. the results of the study are probably

biased, overstating the effectiveness of the diet

100. there are twenty multiple-choice questions on an exam, each having responses a, b, c, or d. each question is worth five points and only one option per question is correct. suppose the student guesses the answer to each question, and the guesses from question to question are independent. the distribution of x= the number of questions the student will get correct, is

binomial

61. a stratified random sample addresses the same issues as which of the following experimental designs?

block design

70. ignoring twins and other multiple births, assume that babies born at a hospital are independent random events with the probability that a baby is a boy and the probability that a baby is a girl both equal to 0.5. the events a= the next two babies are boys and b= the next two babies are girls are

disjoint

46. suppose a straight line is fit to data having response variable y and explanatory variable x. predicting values of y for values of x outside the range of the observed data is called

extrapolation

50. a fisheries biologist studying whitefish in a canadian lake collected data on the length (in centimeters) and egg production for 25 female fish. a scatterplot of her results and computer regression analysis of egg production versus fish length are given below. the equation of the least-squares regression line is

egg(with hat)=-142.74+39.25(length)

40. consider the following scatterplot of the amounts of co (carbon monoxide) and nox (nitrogen oxide) in grams per mile driven in the exhaust of cars. the least-squares regression line has been drawn in the plot. in the scatterplot, the point indicated by the open circle

has a negative value for the residual

33. the height (in feet) and volume (in cubic feet) of usable lumber of 32 cherry trees are measured by a researcher. the goal is to determine if volume of usable lumber can be estimated from the height of a tree. which of the following statements are supported by the scatterplot? i. there is a positive association between height and volume. ii. there is an outlier in the plot. iii. as the height of the cherry tree increases, the volume of usable lumber it yields increases.

i, ii, iii

42. which of the following statements are true about the least-squares regression line? i. the slope is the predicted change in the response variable associated with a unit increase in the explanatory variable ii. the line always passes through the point (x,y), the means of the explanatory and response variables, respectively iii. it is the line that minimizes the sum of the squared residuals

i, ii, iii

45. if removing an observation from a data set would have a marked change on the equation of the least-squares regression line, the point is called

influential

19. jack and jill are both enthusiastic players of a certain computer game. over the past year, jack's mean score when playing the game is 12,400 with a standard deviation of 1500. during the same period, jill's mean score is 14,200 with a standard deviation of 2000. they devise a fair contest: each one will play the game once, and they will compare z-scores. jack gets a score of 14,000, and jill gets a score of 16,000. who won the contest, and what were each of their scores?

jack won- 1.07, jill- .9

97. your friend albert has invented a game involving two ten-sided dice. one of the dice has threes, fours, and fives on its faces, the other has sixes, eights, and tens. he won't tell you how many of each number there are on the faces, but he does tell you that if x= the result of a single roll of the first die and y= the result of a single roll of the second die, then meanx=3.6, sdx=0.8, meany=8.0, sdy=0.9. let z= the sum of the dice when each is rolled once. here's albert's game: you give him $10 each time you roll, and he pays you (in dollars) the amount that comes up on the dice. if p= the amount of money you gain each time you roll, the mean and standard deviation of p are

mean= 1.6, sd= 1.2

99. the mp3 music files on sharon's computer have a mean size of 4.0 megabytes and a standard deviation of 1.8 megabytes. she wants to create a mix of 10 of the songs for a friend. let the random variable t= the total size (in megabytes) for 10 randomly selected songs from sharon's computer. typically, the formula 1.07 (file size)-- 0.02 provides a good estimate of the length of a song in minutes. if m= 1.07t-0.02, what are the mean and standard deviation of m?

mean= 42.78, sd= 6.09

11. you want to use numerical summaries to describe a distribution that is strongly skewed to the left. which combination of measure of center and spread would be the best ones to use?

median and iqr

17. an ecologist who was studying starfish populations collected starfish of the species pisaster was interested in the distributions of the sizes of starfish on a certain shoreline. one measure of size is "arm length." below is a cumulative relative frequency distribution of the arm length of 102 pisaster individuals. the median and iqr of this distribution are approximately

median- 15.2, iqr- 3

41. "least-squares" in the term "least-squares regression line" refers to

minimizing the sum of the squares of all values of the explanatory variable

77. event a occurs with probability 0.3, and event b occurs with probability 0.4. if a and b are independent, we may conclude that

p(a and b)= .12 p(a given b)= .3 p(b given a)= .4 (all of the above)

87. flip a coin four times. if z= the number of heads in four flips, then the probability distribution of z is given in the table below... An expression that represents the probability of at least one tail is

p(z<=3)

66. the reason that blocking (as in a randomized block design) is sometimes used in experimentation is to

reduce variability arising from random assignment

82. the letters p, q, r, and s represent probabilities for the four distinct regions in the venn diagram below. for each question, indicate which expression describes the probability of the event indicated. p(a or b)=

q+s+r

83. the letters p, q, r, and s represent probabilities for the four distinct regions in the venn diagram below. for each question, indicate which expression describes the probability of the event indicated. p(b given a)=

r/(q+r)

3. the histogram below shows the length (in minutes) of 140 songs recorded by the band wilco. which of the following descriptions best fits the distribution?

skewed right with center 4.5 with several high outliers

43. the fraction of the variation in the values of a response y that is explained by the least-squares regression of y on x is the

square of the correlation coefficient

57. in an experiment, an observed effect so large that it would rarely occur by chance is called

statistically significant

60. a public opinion poll in ohio wants to determine whether or not registered voters in the state approve of a measure to ban smoking in all public areas. they select a simple random sample of fifty registered voters from each county in the state and ask whether they approve or disapprove of the measure. this is an example of a

stratified random sample

53. you want to know the opinions of american school teachers about establishing a national test for high school graduation. you obtain a list of the members of the national education association (the largest teachers' union) and mail a questionnaire to 2500 teachers chosen at random from this list. in all 1347 teachers return the questionnaire. the sample is

the 1347 teachers who mailed back the questionnaire

31. when a basketball player makes a pass to a teammate who then scores, he earns an "assist." below is a normal probability plot for the number of assists earned by all players in the nba during the 2010 regular season. which of the following statements about the shape of this distribution is true?

the distribution is skewed right

5. a set of data has a mean that is much larger than the median. which of the following statements is most consistent with this information?

the distribution is skewed right

13. you can roughly locate the mean of a density curve by eye because it is

the point at which the curve would balance if made of solid material

14. you can roughly locate the median of a density curve by eye because it is

the point that divides the area under the curve into two equal parts

35. the correlation coefficient measures

the strength of the linear relationship between two variables

62. in the late 1990s scotland was considering independence from england. an opinion poll showed that 51% of scots favored "independence." another poll taken at the same time showed that only 34% favored being "separate" from england. the reason these results differ by so much is that

the wording of questions has a big effect on poll results

49. a study of child development measures the age (in months) at which a child begins to talk and also the child's score on an ability test given several years later. the study asks whether the age at which a child talks helps predict the test score. the least-squares regression line of test score y on age x is y=110-1.3x. according to this regression line, what happens (on the average) to children who talk one month later than other children?

their predicted test scores go down 1.3 points