AP Statistics Semester 2 Quiz/Checkpoint
Questions
Which of the following is most important for accuracy in inferential statistics? - ANS A
properly drawn random sample
True or False. If we take a properly drawn sample and calculate the mean and standard
deviation, we can estimate the mean of the population and we can come up with a
probability that the true mean falls within a certain interval. - ANS true
Which of the following are key questions in a test of statistical significance?
1. If random chance is the only factor, what's the chance I'll get that result?
2. Is my result so unlikely that something other than chance must be a factor?
3. Am I asking a significant research question? - ANS 1 and 2
Which of the following is a list of common steps to inference? - ANS Identify the study,
be sure the study and your sample are valid, calculate probabilities or confidence
intervals, test for significance
Which of the following are common to all cases of statistical inference?
1. Sample statistics are used to estimate population parameters.
2. Two means are compared.
3. A sample proportion is used to estimate a population proportion. - ANS 1 only
Which of the following indicates the value of (8 2) (.3)^2 (.7)^6? - ANS binompdf(8,.3,2)
You take a 100-question multiple-choice test. Each question has five choices, and you
guess at each question. Which of the following calculator commands would give you the
probability of getting at least 30 questions correct? - ANS 1 - binomcdf(100,.2,29)
(Binomcdf(n, p, x) will sum the individual probabilities from X = 0 through X = x. Since
you want the sum of all possibilities starting at 30, you must subtract the sum of all
possibilities less than 30 from 1.)
,Which of the following are not essential characteristics of a binomial event?
1. Each outcome must be independent.
2. The sample size must be at least 20.
3. A trial can have only two possible outcomes. - ANS 2 only
True or False: The following situation could be considered a binomial experiment: In
1999, 25,000 students took the AP Statistics Exam. The probability that a randomly
selected student from this group passed the exam was about .6. A statistician wants to
know the likelihood that more than 650 out of 1000 students randomly selected from this
group passed the exam. - ANS true
(Even though this situation doesn't strictly fit the definition of a binomial event (there are
no independent trials), it's still a binomial event, since the population is more than 20
times greater than the sample size.)
The probability that a given 80-year-old person will die in the next year is .27. What's the
probability that exactly 10 of 40 80-year-olds will die in the next year? - ANS .1385
(this is binompdf(40,.27,10))
The probability that a given 80-year-old person will die in the next year is .27. What's the
probability that between 10 and 15 (inclusive) of 40 80-year-olds will die in the next
year? - ANS ..6191
(binomcdf(40,.27,15)
Which of the following are true?
1. A binomial event has exactly two possible outcomes.
2. If the population size is at least 20 times the sample size, the independence criteria
for a binomial has been met.
3. As long as the probability for each trial is clearly specified, different trials can have
different probabilities of success. - ANS 1 and 2 only
Consider a binomial event with B(75, .6). Which of the following represents the
probability of getting exactly 50 successes? - ANS (75 50) (.6)^50 (.4)^25
, Fred is a weightlifter who can lift 800 pounds on 45% of his attempts. Which of these
expressions represents the probability Fred will make 30 lifts out of 60? - ANS B(60,
.45, 30)
What's the probability of getting 1 or 3 fives on 10 rolls of a fair die? Hint: Remember the
rule for finding P(A or B). - ANS B(10, 1/6, 1) + B(10, 1/6, 3)
(P(X = 1) is binompdf(10, 1/6, 1) and P(x = 3) is binompdf(10, 1/6, 3). To combine the
two probabilities using or, simply add them: P(X = 1) + P(X = 3) = .323 + .155 = .478.)
Which of the following situations satisfies all the conditions of a binomial setting? (These
conditions are: we know the number of repetitions, the outcome of each trial can be
considered either a success or a failure, we know the probability of success or failure of
any trial, and the probability doesn't change from trial to trial.) - ANS A jar contains 500
balls-300 red and 200 white. Ten balls are randomly selected from the jar, and the
number X of red balls is recorded.
What's the probability of getting exactly 1 five when we roll a fair die 10 times? - ANS
binompdf(10, 1/6, 1) = .323
Suppose you roll a six-sided die 10 times. What's the probability of getting three fives in
those 10 rolls? - ANS .155
(binompdf(10, 1/6, 3))
If you roll a six-sided die 10 times, what's P(x > 3)? - ANS 1-binomcdf(10,1/6,3)
If a success is defined as getting a three on a six-sided die, what's P(x < 3) if you roll
the die 10 times? - ANS binomcdf(10,1/6,2)
A friend of yours can shoot free throws with 75% accuracy (she makes 75% of her
shots). If she attempts 25 free throws, what's the probability she'll make at least 20? -
ANS P(x = 20) + P(x = 21) + P(x = 22) + P(x = 23) + P(x = 24) + P(x = 25)
A friend of yours can shoot free throws with 70% accuracy (she makes 70% of her
shots). If she attempts 25 free throws, what's the probability she'll make fewer than 14?
- ANS P(x < 14)
Under what conditions can you use a normal distribution to approximate the binomial
distribution? - ANS np ≥ 10 and n(1 - p) ≥ 10
Questions
Which of the following is most important for accuracy in inferential statistics? - ANS A
properly drawn random sample
True or False. If we take a properly drawn sample and calculate the mean and standard
deviation, we can estimate the mean of the population and we can come up with a
probability that the true mean falls within a certain interval. - ANS true
Which of the following are key questions in a test of statistical significance?
1. If random chance is the only factor, what's the chance I'll get that result?
2. Is my result so unlikely that something other than chance must be a factor?
3. Am I asking a significant research question? - ANS 1 and 2
Which of the following is a list of common steps to inference? - ANS Identify the study,
be sure the study and your sample are valid, calculate probabilities or confidence
intervals, test for significance
Which of the following are common to all cases of statistical inference?
1. Sample statistics are used to estimate population parameters.
2. Two means are compared.
3. A sample proportion is used to estimate a population proportion. - ANS 1 only
Which of the following indicates the value of (8 2) (.3)^2 (.7)^6? - ANS binompdf(8,.3,2)
You take a 100-question multiple-choice test. Each question has five choices, and you
guess at each question. Which of the following calculator commands would give you the
probability of getting at least 30 questions correct? - ANS 1 - binomcdf(100,.2,29)
(Binomcdf(n, p, x) will sum the individual probabilities from X = 0 through X = x. Since
you want the sum of all possibilities starting at 30, you must subtract the sum of all
possibilities less than 30 from 1.)
,Which of the following are not essential characteristics of a binomial event?
1. Each outcome must be independent.
2. The sample size must be at least 20.
3. A trial can have only two possible outcomes. - ANS 2 only
True or False: The following situation could be considered a binomial experiment: In
1999, 25,000 students took the AP Statistics Exam. The probability that a randomly
selected student from this group passed the exam was about .6. A statistician wants to
know the likelihood that more than 650 out of 1000 students randomly selected from this
group passed the exam. - ANS true
(Even though this situation doesn't strictly fit the definition of a binomial event (there are
no independent trials), it's still a binomial event, since the population is more than 20
times greater than the sample size.)
The probability that a given 80-year-old person will die in the next year is .27. What's the
probability that exactly 10 of 40 80-year-olds will die in the next year? - ANS .1385
(this is binompdf(40,.27,10))
The probability that a given 80-year-old person will die in the next year is .27. What's the
probability that between 10 and 15 (inclusive) of 40 80-year-olds will die in the next
year? - ANS ..6191
(binomcdf(40,.27,15)
Which of the following are true?
1. A binomial event has exactly two possible outcomes.
2. If the population size is at least 20 times the sample size, the independence criteria
for a binomial has been met.
3. As long as the probability for each trial is clearly specified, different trials can have
different probabilities of success. - ANS 1 and 2 only
Consider a binomial event with B(75, .6). Which of the following represents the
probability of getting exactly 50 successes? - ANS (75 50) (.6)^50 (.4)^25
, Fred is a weightlifter who can lift 800 pounds on 45% of his attempts. Which of these
expressions represents the probability Fred will make 30 lifts out of 60? - ANS B(60,
.45, 30)
What's the probability of getting 1 or 3 fives on 10 rolls of a fair die? Hint: Remember the
rule for finding P(A or B). - ANS B(10, 1/6, 1) + B(10, 1/6, 3)
(P(X = 1) is binompdf(10, 1/6, 1) and P(x = 3) is binompdf(10, 1/6, 3). To combine the
two probabilities using or, simply add them: P(X = 1) + P(X = 3) = .323 + .155 = .478.)
Which of the following situations satisfies all the conditions of a binomial setting? (These
conditions are: we know the number of repetitions, the outcome of each trial can be
considered either a success or a failure, we know the probability of success or failure of
any trial, and the probability doesn't change from trial to trial.) - ANS A jar contains 500
balls-300 red and 200 white. Ten balls are randomly selected from the jar, and the
number X of red balls is recorded.
What's the probability of getting exactly 1 five when we roll a fair die 10 times? - ANS
binompdf(10, 1/6, 1) = .323
Suppose you roll a six-sided die 10 times. What's the probability of getting three fives in
those 10 rolls? - ANS .155
(binompdf(10, 1/6, 3))
If you roll a six-sided die 10 times, what's P(x > 3)? - ANS 1-binomcdf(10,1/6,3)
If a success is defined as getting a three on a six-sided die, what's P(x < 3) if you roll
the die 10 times? - ANS binomcdf(10,1/6,2)
A friend of yours can shoot free throws with 75% accuracy (she makes 75% of her
shots). If she attempts 25 free throws, what's the probability she'll make at least 20? -
ANS P(x = 20) + P(x = 21) + P(x = 22) + P(x = 23) + P(x = 24) + P(x = 25)
A friend of yours can shoot free throws with 70% accuracy (she makes 70% of her
shots). If she attempts 25 free throws, what's the probability she'll make fewer than 14?
- ANS P(x < 14)
Under what conditions can you use a normal distribution to approximate the binomial
distribution? - ANS np ≥ 10 and n(1 - p) ≥ 10
