``
Week 1: 1, 3, 22, 23, 24, 25, 32, 41, 43, 45, 50, 51, 52, 54, 55
Week 2: MW class: 11ab , 16, 58, 59
Friday Class 11, 16, 20, 26, 40, 57, 58, 59
Week 3: MW class 2. 4, 10, 11c, 26, 35a, 36 I, d, 40, 44 (for b, find Q1, Q2, Q3 only), 57, 60
Friday class 4, 5, 6, 7, 8, 12, 17, 21, 34, 35a 36 I, d, 37, 37, 39, 42, 44, 49, 60
Week 4:
Week 5
1, 2, 3, ,10, 11, 16, 20, 22, 23, 24, 25, 26, 28, 32, 41, 43, 45, 46, 50, 51, 52, 53, 54, 55
Exam I ; All the problems
1)Give an example of a continuous random variable.
2)IQ scores have a mean 100 and a standard deviation 16. Is an IQ score of 150 unusual?
3)Describe the sampling method used for each of the following:
a)From a list of 1000 ID numbers, choose a starting point by chance and then select every 10th ID number.
b)25 students are randomly selected from each grade level at a high school and surveyed about their study habits.
4)The following data points are the test scores for a statistics class. Compute each of the following:
a) b) percentile of 13 c)
50 18 13 80 14 38 11 13 39 41
5)Are the following events a) independent b) disjoint? Justify your answer.
i) A: Selecting a person under 24 years old.
B: Selecting a person earns less than $20,000.
ii)
A: Selecting a male college student.
B: Selecting an adult man who works part-time.
6)At a small four-year college, all freshmen and sophomores are required to enroll in exactly one of the following math classes: Math I, Math II or Math III. 200 freshmen and 450 sophomores are enrolled in Math I, 350 freshmen and 400 sophomores are enrolled in Math II, and 250 freshmen and 300 sophomores are enrolled in Math III. a) Find the probability that a randomly chosen person is either a freshman or enrolled in Math II. b) Find the probability that a randomly chosen person is taking Math I given that he is a sophomore. c) When two students are chosen randomly, find the probability that they are both freshmen and enrolled in Math I.
7)Through a manufacturing error, three cans marked “regular soda” were accidentally filled with diet soda and placed into a 12-pack. When 2 cans are randomly chosen from the 12-pack without replacement, find the probability of selecting a) two diet soda cans b) at least one diet soda c)exactly one diet can.
8) A student experiences difficulties with malfunctioning alarm clocks. Instead of using one alarm clock, he decides to use four. a) What is the probability that at least one alarm clock works correctly if each clock has a 95% chance of working correctly? b) Find the probability that all of the clocks work correctly. c) Find the probability that exactly three clocks work correctly.
9)A) When 5 babies are born, how many different gender sequences are possible? B) When 5 dice are rolled, how many different outcomes are possible?
10) Compute the sample standard deviation: x = 1, 5, 8, 10 and the sample z-score of 10.
11)
Class / Frequency1.3-1.8 / 2
1.9-2.4 / 12
2.5-3.0 / 6
a)Construct a relative frequency histogram
b)Construct a cumulative distribution table
c)Compute the mean.
12)A batch of 50 calculators contains 5 defective calculators. When 3 calculators are selected at random without replacement, what is the probability that a) all 3 calculators are defective b) at least one calculator is defective, c) exactly two calculators are defective.
13)A magazine editor must choose 4 short stories for this month’s issue from 30 submissions. In how many ways can the editor choose this month’s stories?
14)When five cards are drawn without replacement from a standard deck of 52 cards, find the probability of obtaining exactly two kings.
15)Find the probability of selecting six winning numbers from 1 to 51.
16)
5, 9, 11, 14, 15, 17, 19, 23
a)Construct a frequency table using 5 as a starting point and class width of 7.
b)Construct a relativefrequency histogram.
c)Construct a cumulative distribution table
17)The following table data are characteristics of voting-age population regarding a recent election.
A Voted / Did not voteB Males / 230 / 400
Females / 370 / 240
a)When a person is chosen at random, find the probability that the person did not vote, given that the person is female.
b)When a person is chosen at random, find the probability that the person is female or voted.
c)When two people are chosen without replacement, find the probability of choosing two males who voted.
18)65 percent of residents in Greenville, PA are women. When 3 people are selected at random, find the probability that a) at least one woman is selected b) none of the women is selected.
19)A) How many different area code 909 telephone numbers are possible?(you may assumethat the first digit of any phone number cannot be 0 or 1) B) Suppose a computer requires eight characters for a password. The first three characters must be letters and the remaining five characters must be numbers. How many passwords are possible?
20)Use the following frequency table to compute the mean:
Class / Frequency0-4 / 6
5-9 / 7
21)A case of 10 bottles of wines contains 7 Merlot and 3 Cabernet. 3 bottles are chosen randomly WITH replacement .
a)Find the probability that all 3 are Merlot. b) Find the probability that at least one is Merlot.
22)(2 points each) The average annual salary of Mt. SAC professors is $23,000.
a)Identify the population of the study.
b)Is $23,000 a parameter or statistic? Justify your answer.
c)Is $23,000 quantitative or categorical? Justify your answer.
23) Identify the sampling method used:: An social scientist is studying the effect of education on salary and conducts a survey of 200 selected workers from each of the following categories: less than a high school degree; high school degree; more than high school degree.
24) A researcher wants to investigate a correlation between meth use as a teen, and having marital problems as an adult.
a)Identify the population.
b)What are the two groups that are being compared?
c)What is the explanatory variable? What is the response?
d)Find a confounding variable.
e)Which type of study is more appropriate: observational or experimental? Justify your answer
25)A study finds that the average cost of a gym membership in the US is $34 a month. Is $34 a parameter or statistic? Justify your answer.
26)( 3 points) Locate the mean, median and mode for the graph shown below:
Median ___ Mode______Mean______
27)In how many ways can 8 people be arranged for a photograph session?
28)Identify the sampling technique used in the following study: In an effort to determine customer satisfaction, Delta Airline randomly select 59 flights during certain week and survey some passengers on those flights.
29)Suppose 40 cars start at a car race. How many ways can the top three cars finish the race?
30)A machine has a probability 0.03 of producing a defective golf ball. When 3 golf balls are manufactured by this machine, find the probability that none of the golf balls is defective.
31)When three people are selected randomly, find the probability that their birthdays are all different.
32)The mean credit card debt for college students in the U.S. is $2100. Is 2100 a parameter or statistic? Justify your answer.
33)How many different outcomes are possible when 3 dice and 2 coins are tossed?
34)Determine whether the following events are a) disjoint b) independent or dependent
A)Randomly selecting a male driver who weighs less than 140 pounds
B)Randomly selecting a male driver who has more than three speeding tickets.
35)(2 points each) Fill in the blank
a)If the distribution of a random variable is skewed to the right, the value of the mean is ______than the value of the median.
b)A ______sample is the one in which respondents themselves decide whether to be included in the sample and often reflects opinions of those with strong interests.
c)A binomial experiment requires that a ______number of trials are performed, each trial has two possible outcomes, the trials are ______, and the probability of success remains the same.
d)The running time of a randomly selected movie is an example of ______random variable.
e) A researcher divides the population into three groups by their incomes: low, medium, and high. Then he selects a random sample from each group. He used ______sampling method in this study.
f)There are ______possible outcomes when a coin is tossed 6 times.
36)
a)A correlation between two variables does not imply one is a ______of the other.
b)In a ______study, data are collected from the past by going back in time.
c)In ______sampling method, every nth item is selected.
d)A ______is a numerical measurement of a population.
e)A value is unusual if its z-score is more than ______or less than ______.
f)To apply the 68-95-99.7 principle, the distribution of the variable must be ______-______.
g)When the effects of one factor cannot be separated from the effects of some other factors, the effects are said to be______.
h)When the researcher controls the assignment of members to different groups, the study is ______study .
i)True/false: If the distribution is skewed, we are usually better off with the mean than the median.
37)A recent study finds that 34% of adult American males are obese. Based on this study, what is the probability that all 3 are obese when 3 adult American males are chosen randomly?
38) How many different social security numbers with the last four digits 1234 are possible?
39)A random sample of 300 Mt. SAC students majoring in math or psychology is selected. These students were asked whether they are happy with their majors. The results are summarized in the following table:
Happy / UnhappyMath / 100 / 20
Psychology / 10 / 170
a)When one student is selected randomly from this group, find the probability this student is happy with the choice of major given that the student is a math major.
b)When two students are chosen randomly, find the probability that they are both math majors.
40)(3 points) Choose the data set with a smaller standard deviation. Justify your answer.
A)The IQ scores of all Mt. SAC students.
B)The IQ scores of all Mt. SAC students majoring in mathematics.
41)(3 points) I
A retail store manager wants to conducts a study regarding the shopping habits of his customers. He selects 60 customers who enter his store on a Tuesday morning.
a)Identify the sampling method used in the study.
b)Is the sample representative of the population? Justify your answer.
42)( 3 points) Determine whether the following events are dependent or independent. Justify your answer.
A :You eat fast food for dinner every night.
B: You gain weight.
43)Researchers wanted to determine if there is a correction between coffee consumption and the occurrence of skin cancer on women. The researchers looked at 10,000 women and asked them to report their coffee drinking habits.
a) Is this an observational or an experimental study?
b)Find the explanatory variable and the response variable.
c)Can you conclude that coffee drinking causes skin cancer?
d)Which type of study would you use: cross sectional, prospective or retrospective?
44)Compute a) percentile of 21 b) box plot c) for the following 12 values
14 16 21 34 38 39 41 45 50 53 82 90
45)A study finds male children born to women who smoke during pregnancy run a higher risk of criminal behaviors that last into adulthood than male children born to women who do not smoke.
a)Determine whether this study is observational or experimental.
b)What are the groups that are being compared?
c)What is the explanatory variable and what is the response variable?
d)Find a confounding variable.
e) Can we say smoking during pregnancy is responsible for higher criminal behavior? Justify your answer.
46)3 points) Identify the sampling method used: A random sample of 100 people from each of five different age categories was selected.
47)From a group of 80 people, a jury of 12 people is selected. In how many ways can a jury of 12 people be selected?
48)In a group of 10 persons, 4 have a Type A personality and 6 have a type B personality. When three people are chosen randomly without replacement, find the probability that at least one person has a Type A personality
49)(3 points) Determine whether the following events are independent or dependent. Justify your answer.
A: USC wins a football game.
B: You get a high score on a statistic exam
50)A question is posed on the ESPN website asked visitors to the site to say whether they thought that marijuana should be legally available for medical purposes.
a)Identify the population.
b)Identify the sample.
c)Is the study cross sectional, prospective, or retrospective? Justify your answer.
d)Is the sample likely to be representative of the population? Justify your answer.
51)A department store mails a customer satisfaction survey to people who make credit card purchases at the store. Surveys are mailed to 1000 randomly chosen people, and 80 people returned the survey.
f)Identify the population.
g)What is the sample?
h)Is the sample likely representative of the population? Justify your answer.
52) The MLB reports that the average annual salary of the major league baseball players is $5,100,000.
a)Identify the population of the study.
b)Is $5.1M a parameter or statistic? Justify your answer.
53)(3points) Determine whether the following variable is discrete or continuous. Justify your answer.
Lifetime of a TI 84 calculator
54)(2 points) Classify the following variable as quantitative or categorical:
Colors of baseball uniforms.
55) In a recent study, subjects were randomly assigned to two groups, and one group was given an herb and the other group a placebo. After 6 months, the numbers of respiratory tract infections each group had were compared.
a) Is the study cross sectional, prospective, or retrospective? Justify your answer.
b)What is the explanatory variable and what is the response variable?
c)Is the study observational or experimental? Justify your answer.
d)Is the study cross sectional, retrospective, or prospective?
56)
a ) True/false In an observational study, a definite cause-and-effect cannot be shown
c)In an experimental study, the subjects in the ______group receive a dummy treatment, enabling the researchers to control for the placebo effect.
57)( 4 points) Use the formula to compute the standard deviation for x=1, 8, 11, 12
58)(5 points) Construct a frequency table for the values shown below. Begin with a lower class limit of 1.0 and use a class width 0.4.
1.2 1.2 1.4 1.6 1.9 2.1 2.2 2.4 2.4
59) (6 points)
GPA / Frequency / Class Boundaries / Relative Frequency / Class Midpoint1.0-1.9 / 12
2.0-2.9 / 5
3.0-3.9 / 3
Complete the table and construct a relative frequency histogram. In addition, construct a cumulative distribution table.
60)For the following 11 values, find a) b) c) percentile of 50
21 23 26 29 31 33 37 39 40 50 54
61)Find the z-score of 40 id the mean is 30 and a standard deviation is 6
Answers (Warning: I have minor brain damage. Some answers may not be correct.)
1)x = height of a man is an example of a continuous random variable.
2)Yes, its z-score is 3.13, which is more than 2.
3)A) systematic b) stratified
4)a), a whole number. Thus b) percentile of 13= c) , a decimal number. Thus take 8th value, which
5)i) a) They are not disjoint. There are many people under the age of 24 who make less than $20,000. b) They are dependent. The probability that a person under 24 makes under $20,000 is much higher than that of the general population.
ii) a) They are not disjoint. B) They are dependent as college students are more likely to work part-time than the general population
6)a) b) c)
Math I / Math II / Math IIIFreshmen / 200 / 350 / 250
Sophomores / 450 / 400 / 300
7)a) b) c)
8)a) b) c) Use the binomial formula or observe there are 4 possible sequences for this event.
9)A) 32 B) (make 5 boxes. There are 6 possible outcomes for each die.)
10)
X /1 /
5 /
8 /
10 /
, the sample z-score of 10 is
11)
Frequency / Class Bd / Midpoint / Freq(mid)1.3-1.8 / 2 / 1.25-1.85 / 1.55 / 3.1
1.9-2.4 / 12 / 1.85-2.45 / 2.15 / 25.8
2.5-3.0 / 6 / 2.45-3.05 / 2.75 / 16.5
N=20 /
The mean is 45.4/20=2.27
Cumulative Distribution
FrequencyLess than or equal to 1.8 / 2
Less than or equal to 2.4 / 14
Less than or equal to 3.0 / 20
12)a) b) c) or
13) ( without replacement, the order does not matter)
14) You must choose 2 kings and 3 non-kings. There are four kings and 48 non-kings.
15)a)
16)Use class boundaries for the histogram
Frequency / Class Boundaries / Class midpoint / Relative frequency5-11 / 3 / 4.5-11.5 / 8 / 37.5%
12-18 / 3 / 11.5-18.5 / 15 / 37.5%
19-25 / 2 / 18.5-25.5 / 22 / 25%
Frequency
Less than or equal to 11 / 3
Less than or equal to 18 / 6
1 Less than or equal to 25 / 8
17)a) b) c)
18)a)for at least one, use complement: first find the probability that all three are men. Then subtract from 1. b) This is just the probability of all three are men.
19)(the order matters, with replacement: use the counting principle. Make 7 boxes, the first digit must be 2-9 so there are only 8 choices. ) b)
20)
Frequency / Class midpoint / (Class mid)(freq)0-4 / 6 / 2 / 12
5-9 / 7 / 7 / 49
The mean is 61//13=4.7
21)a) b)
22) ) a) all Mt, SAC professors. B) $23,000 is more likely to be a parameter. The salaries of Mt. SAC professors are available to the public. C) quantitative: salaries can be measured numerically.
23) This is stratified: a random sample is taken from each subgroup.
24) A) all married adults Bs ) Married adults who used meth as teen vs. married adults who did not use meth as teens C) Explanatory: whether used meth as a teen or not. Response: marital problems D) educational level, income E) observational; it is unethical to make people in the control group use meth.
25) Statistic: it is impossible to survey ALL the gyms in the U.S.
26) Medan: A mode: B mean C: The mode is the highest point of the graph. The mean is to the right of the median (the distribution is skewed to the right)
27) This is permutation: the order matters (different order produces different pictures and without replacement). 8(7)(6)…(1) = 40320 or
28) Cluster: here the subgroups are the flights. Random samples are taken from some of the subgroups, not all.
29) oruse permutation since the order matters and without replacement
30) : they can be treated as independent events, so make three boxes. The probability of a golfball not defective is 1-0.03-=0.97. Then multiply this number three times).
31) (the birthday of the first person can be any day, thus there are 365 choices. The birthday of the second person must be different from the first person, thus there are 364 choices. The third birthday must be different from the first two. There are 363 choices)
32) this is a statistics. It must be computed from the sample as the population is too large.
33) use the counting principle: the order matters, with replacement: 6 possible outcomes for a die, 2 for a coin,
34) They are not disjoint. They are independent: The weight of a person does not affect his driving skills.