AP STAT FINAL STUDY GUIDE
Let the random variable X represent the amount of money Dan makes doing lawn care in a randomly selected week in the summer. Assume that X is Normal with mean $240 and standard deviation $60. The probability is approximately 0.6 that, in a randomly selected week, Dan will make less than
$255
A randomly selected student is asked to respond Yes, No, or Maybe to the question "Do you intend to vote in the next presidential election?" The sample space is { Yes, No, Maybe }. Which of the following represents a legitimate assignment of probabilities for this sample space?
0.4, 0.4, 0.2
The mean and standard deviation of the number of contaminated chickens in a crate are
m= 7.2; s = 2.24
Event A occurs with probability 0.2. Event B occurs with probability 0.8. If A and B are disjoint (mutually exclusive), then
P(A or B) = 1.0
A recent investigation of prices for five-year-old Toyota Camrys in Montgomery, Alabama, and New York, New York, revealed that the mean price in Montgomery was $13,200 with a standard deviation of $1000. In New York, the mean price was $12,800 with a standard deviation of $1800. Which of the following statements is true?
The standard score for a car priced at $15,000 would be higher in Montgomery than in New York.
The probability of any outcome of a random phenomenon is
the proportion of times the outcome occurs in a very long series of repetitions.
You select one musician from this group at random. What is the probability that this person plays a woodwind?
0.159
All of the following small data sets have a mean of 5. Which one has the lowest standard deviation?
1 3 5 5 5 7 9
A die is loaded so that the number 6 comes up three times as often as any other number. What is the probability of rolling a 1 or a 6?
1/2
A medical researcher collects health data on many women in each of several countries. One of the variables measured for each woman in the study is her weight in pounds. The following list gives the five-number summary for the weights of adult women in one of the countries. Country A: 92, 110, 120, 160, 240 About what percent of Country A women weigh between 110 and 240 pounds?
75%
We say that the design of a study is biased if which of the following is true?
Certain outcomes are systematically favored.
A study examined the relationship between the sepal length and sepal width for two varieties of an exotic tropical plant. Varieties X and O are represented by x's and o's, respectively, in the following scatterplot. Which of the following statements is true?
Considering each variety separately, there is a negative correlation between sepal length and width
A forester studying oak trees finds that the correlation between x = the ages (measured in years) and y = height (in feet) of a sample of trees is 0.78. Which of the following statements must be true?
If we measure the height in meters instead of feet, the correlation would still be 0.78.
You select one student from this group at random. Which of the following statement is true about the events "Typically walks to school" and "Junior?"
The events are not mutually exclusive but they are independent.
A recent survey by a Canadian magazine on the contribution of universities to the economy was circulated to 394 people who the magazine decided "are the most likely to know how important universities are to the Canadian economy." Which of the following is the main problem with using these results to draw conclusions about the general public's perception?
Lack of random selection
The bar graph at right shows the distribution of breeds for all the champions of the annual World Canine Disc Championships from 1975 to 2009. Which of the following statement can be made on the basis of this graph?
The graph exaggerates the difference between the number of champions of each breed category
A biology teacher has just finished grading a quiz for a class of 26 students and has calculated measures of center and spread on the scores. While writing the grades on the quizzes, he realizes he made a mistake, and the highest grade should be 10 points higher. Which one of the following sets of measurements will he have to recalculate?
The mean and standard deviation
If a distribution is skewed to the right, which of the following is true?
The mean must be greater than the median.
Which of the following random variables is geometric?
The number of digits I will read beginning at a randomly selected starting point in a table of random digits until I find a 7.
The following bar graph gives the percent of owners of three brands of trucks who are satisfied with their truck. From this graph, we may conclude that
There are only small differences in the satisfaction of owners for the three brands
In a large population of college students, 20% of the students have experienced feelings of math anxiety. If you take a random sample of 10 students from this population, the mean and standard deviation of the number of students in the sample who have experienced math anxiety is:
m=2; s=1.265
Which of the following is a method for improving the accuracy of a sample?
Use large sample sizes.
The graph below shows how mothers of young children respond to the question, "How many times a week do you choose fast food as a dining option for your family?" What's wrong with this method of presenting information?
Using proportionally-sized hamburgers exaggerates differences between responses.
We wish to draw a sample of 5 without replacement from a population of 50 households. Suppose the households are numbered 01, 02, . . . , 50, and suppose that the relevant line of the random number table is 11362 35692 96237 90842 46843 62719 64049 17823. Then the households selected are
households 11 36 23 08 42
At the beginning of the school year, a high-school teacher asks every student in her classes to fill out a survey that asks for their age, gender, the number of years they have lived at their current address, their favorite school subject, and whether they plan to go to college after high school. Which of the following best describes the variables that are being measured?
three categorical variables and two quantitative variables
X and Y are independent random variables, and a and b are constants. Which one of the following statements is true?
Var(X − Y) = Var(X) + Var(Y)
Experience has shown that a certain lie detector will show a positive reading (indicates a lie) 10% of the time when a person is telling the truth and 95% of the time when a person is lying. Suppose that a random sample of 5 suspects is subjected to a lie detector test regarding a recent one-person crime. Then the probability of observing no positive readings if all suspects plead innocent and are telling the truth is
0.591.
A fair coin is tossed four times, and each time the coin lands heads up. If the coin is then tossed 1996 more times, how many heads are most likely to appear in these 1996 additional tosses?
998
The weights of adult male Labrador Retrievers are approximately Normally distributed with a mean of 87 pounds and a standard deviation of 8 pounds. Which of the following statements is true?
The proportion of adult male Labrador Retrievers that weigh less than 80 pounds is approximately equal to the proportion that weigh more 94 pounds
A sample of 250 high school students were asked, "If you had $1000 to contribute to one kind of charitable organization, which type of organization would you choose?" Below is a two-way table of responses to this question and gender.
The proportion of males who said they would contribute to an environmental organization was higher than the proportion of females who said they would contribute such an organization.
A marketing survey compiled data on the total number of televisions in households. If X = the number of televisions in a randomly-selected household, and we omit the rare cases of more than 5 televisions, then X has the following distribution: What is the probability that a randomly chosen household has at least two televisions?
0.39
If PA. = 0.24 and PB. = 0.52 and A and B are independent, what is P(A or B)?
0.6352
Here are the IQ test scores of 10 randomly chosen fifth-grade students: 145 139 126 122 125 130 96 110 118 118 To make a stemplot of these scores, you would use as stems
09, 10, 11, 12, 13, and 14
One flight—Philadelphia to West Palm Beach, FL—is 953 miles long and costs $110. Which of the following expressions correctly represents the residual for this data point?
110 − (101.24 + 0.02977 ⋅ 953)
For a certain experiment you have 8 subjects, of which 4 are female and 4 are male. The name of the subjects are listed below: Males: Atwater, Bacon, Chu, Diaz. Females: Johnson, King, Liu, Moore There are to be two treatment groups, A and B. If a randomized block design is used, with the subjects blocked by their gender, which of the following is not a possible group of subjects for treatment group A?
Atwater, Bacon, Chu, Johnson
A vending machine operator has determined that the number of candy bars sold per week by a certain machine is a random variable with mean 125 and standard deviation 7. His profit on each bar sold is $0.25, and it costs him $5.00 per week to maintain the machine and rent the space for it. What are the mean and standard deviation for Y = the profit he earns from this machine in a randomly-selected week?
Mean = 26.25, Standard deviation $1.75
A sample of student opinion at a Big Ten university selects an SRS of 200 of the 30,000 undergraduate students and a separate SRS of 100 of the 5,000 graduate students. What is the term for this kind of sample?
Stratified random sample
At right are box plots describing the distribution of prices paid for homes in two suburbs of Columbus, Ohio over a single 30-day period in 2012. Which of the following statements is supported by the information in this graph?
The median house price in Dublin is higher than the 75th percentile of house price in Westerville.
To test the effect of music on productivity, a group of assembly line workers are given portable mp3 players to play whatever music they choose while working for one month. For another month, they work without music. The order of the two treatments for each worker is determined randomly. This is
a matched pairs experiment
Other things being equal, larger automobile engines are less fuel-efficient. You are planning an experiment to study the effect of engine size (in liters) on the fuel efficiency (in miles per gallon) of sport utility vehicles. In this study
gas mileage is a response variable, and you expect to find a negative association
There are 10 red marbles and 8 green marbles in a jar. If you take three marbles from the jar (without replacement), the probability that they are all red is:
0.147
Jun and Deron are applying for summer jobs at a local restaurant. After interviewing them, the restaurant owner says, "The probability that I hire Jun is 0.7, and the probability that I hire Deron is 0.4. The probability that I hire at least one of you is 0.9." What is the probability that both Jun and Deron get hired?
0.2
In 1965, the mean price of a new car was $2,650 and the standard deviation was $1000. In 2011, the mean was $30,500 and the standard deviation was $9000. If a Ford Mustang cost $2300 in 1965 and $28,000 in 2011, in which year was it more expensive relative to other cars?
2011, because the standard score is higher than in 1965
The mean birth weight of infants born at a certain hospital in the month of April was 128 oz. with a standard deviation of 10.2 oz. Which of the following is a correct interpretation of standard deviation?
The distance between the weight of each infant bon in April and the mean weight was, on average, about 10.2 oz.
A sample of 99 distances has a mean of 24 feet and a median of 24.5 feet. Unfortunately, it has just been discovered that the maximum value in the distribution, which was erroneously recorded as 40, actually had a value of 50. If we make this correction to the data, then
the median remains the same, but the mean is increased.
Which of the following is closest to the 61st percentile of a standard Normal distribution?
z = 0.28
In order to set premiums at profitable levels, insurance companies must estimate how much they will have to pay in claims on cars of each make and model, based on the value of the car and how much damage it sustains in accidents. Let C be a random variable that represents the cost of a randomly selected car of one model to the insurance company. The probability distribution of C is given below. C $0 $1000 $4000 $10,000 PC. 0.60 0.05 0.13 0.22 .The probability that the insurance company will have to pay a claim of at least $1000 for a randomly selected car is:
0.40
In the town of Tower Hill, the number of cell phones in a household is a random variable W with the following distribution: W 0 1 2 3 4 5 P(W) 0.1 0.1 0.25 0.3 0.2 0.05 The probability that a randomly-selected household has at least two cell phones is
0.80
It has been estimated that about 30% of frozen chickens are contaminated with enough salmonella bacteria to cause illness if improperly cooked. Chickens are delivered to grocery stores in crates of 24. Assume the chickens are independently selected for inclusion in the crate. The probability that a certain crate has more than 4 contaminated chickens is
0.8889
The cumulative relative frequency graph at right shows the distribution of lifespans for 39 U.S. presidents. Which of the following is closest to the 70th percentile of this distribution?
77 years
You randomly select one truck owner. What is the probability that he owns a Dodge or has four wheel drive?
90/125
The five-number summary for scores on a statistics exam is 11, 35, 61, 70, 79. In all, 380 students took the test. About how many had scores between 35 and 61?
95
1200 tomatoes have a mean weight of 143 grams and a standard deviation of 35 grams. If the weights are Normally distributed, approximately how many tomatoes weight between 73 grams and 178 grams?
978
Jen's commute to work requires that she take the Blue subway line, then transfer to the Red line. The length of the trip on the Blue line has a mean of 18 minutes with a standard deviation of 2 minutes. The Red line trip takes 12 minutes with a standard deviation of 1 minute. The waiting time between when she gets off the Blue line and her Red line train arrives has mean of 10 minutes and a standard deviation of 5 minutes. Assume (perhaps unrealistically) that these times are independent random variables. What are the mean and standard deviation of her entire commute?
Mean = 40 minutes; Standard deviation = 5.48 minutes
A small company estimating its photocopying expenses finds that the mean number of copies made per day for the past 12 months is 258 copies per day with a standard deviation of 24 copies per day. Which of the following is a correct interpretation of standard deviation?
On average, the number of copies made each day was about 24 copies per day away from the mean, 258
All but one of the following statements contains an error. Which statement could be correct?
The correlation between mid-August soil moisture and the per-acre yield of tomatoes is r = 0.53.
Which of the following statements about standard deviation is true?
Standard deviation is always a non-negative number
One hundred people work at Lagtime Internet Services. Suppose after a particularly successful year, the president of the company decided to double his own salary and not change anyone else's. Assuming the president makes more than anyone else, which of the following statements about changes in measures of center and spread is true?
The mean and standard deviation will increase, but the median and interquartile range will stay the same
When testing water for chemical impurities, results are often reported as bdl, that is, below detection limit. The following are the measurements of the amount of lead in a series of water samples taken from inner-city households (in parts per million): 5, 7, 12, bdl, 10, 8, bdl, 20, 6 Which of the following statements can we be sure is true?
The median lead level in the water is 7 ppm.
A researcher reports that the participants in his study lost a mean of 10.4 pounds after two months on his new diet. A friend of yours comments that she tried the diet for two months and lost no weight, so clearly the report was a fraud. Which of the following statements is correct?
The report gives only the mean. This does not imply that all participants in the study lost 10.4 pounds or even that all lost weight. Your friend's experience does not necessarily contradict the study results.
The least squares regression line minimizes which one of the following quantities?
The sum of the squared differences between the observed values of the response variable and the predicted values of the response variable
We may conclude that
either A or B always occurs
On May 11, 50 randomly selected subjects had their systolic blood pressure (SBP) recorded twice—the first time at about 9:00 a.m. and the second time at about 2:00 p.m. If one were to examine the relationship between the morning and afternoon readings, then one might expect the correlation to be
high and positive, as those with relatively high readings in the morning will tend to have relatively high readings in the afternoon.
An event A will occur with probability 0.5. An event B will occur with probability 0.6. The probability that both A and B will occur is 0.1. The conditional probability of A, given B
is 1/6
