AP Stat, Midterm
The number of tickets purchased by a customer for the Ice Hogs game at BMO Harris Bank center can be considered a random variable. The table below shows the relative frequency distributions (check packet). Suppose each ticket for the game cost $12. Based on the distribution shown, what is the mean cost per costumer for the game?
$29.40
The number of hybrid cars a dealer sells weakly has the following probability distribution (check packet). The dealer purchases the cars for $21,000 and cells them for $24,500. What is the expected weekly profit from selling hybrid cars?
$5,355
Supposed P(X) = .25 and P(Y) = .45. If P(X|Y) = .20, what is P(Y|X)?
.32
A random variable Y has the following probability distribution (check packet). The value of the constant C is
0.15
A tropical storm is classified as major if it has sustained winds greater than 110 miles per hour. Based on data from the past two decades, a meteorologist estimated the following percentages about future storms. (check packet) Based on the meteorologists estimates, approximately what is the probability that a future tropical storm will originate in the Pacific Ocean and be classified as major?
0.170
Let the random variable X represent the profit made on a randomly selected day by a certain store. Assume that X is Normal with mean $360 and a standard deviation $50. What is P(X>$400)?
0.2119
(check packet for table) find the probability of a randomly drawn marble being yellow, given that the marble is small.
0.39
A marketing survey compiled data on the number of cars in households. If X = the number of cars in a randomly selected household, and we omit the rare cases of more than 5 cars, the X has the following probability distribution (check packet). What is the probability that a randomly chosen household has at least two cars?
0.39
(check packet for table) What is the probability that a randomly selected marble will be blue or white?
0.50
In the town of Lakeville, the number of cell phones in a household is a random variable W with the following probability distribution (check packet). The standard deviation of the number of cell phones in a randomly selected home is
1.32
Using the problem above, what is the expected value of the number of cars in a randomly selected household?
1.45
As part of a study on the relationship between the use of tanning booths and the occurrence of skin cancer, researchers reviewed the medial records of 1,436 people. The table below summarizes tanning booth use for people in the study who did and did not have skin cancer. Of the people in the study who had skin cancer, what fraction used a tanning booth?
190/896
Supposed the scores on an exam have a mean of 75 with a standard deviation of 8. If one student has a test result with a z-score of -1.5, and a second student has a test result with a z-score of 2.0, how many points higher was the second student's result than that of the first?
28
the mean of a data set is 40 pounds and the standard deviation is 8 pounds. What value of an observation corresponds to a z-score of -1.25
30
A business evaluates a proposed venture as follows. it stands to make a profit of $10,000 with probability 3/20, to make a profit of $5,000 with probability of 9.20, to break even with probability of 5/20, and to lose $5,000 with probability 3/20. The expected profit in dollars is
3000
Which of the following distributions has a mean of 60 and a standard deviation of 4?
48 is on the left side, 60 is the center, and 72 is on the right side
Using the empirical rule, you can assume that what percent of the normal distribution is outside two standard deviations of the mean in both directions?
5%
Suppose X and Y are independent random variables. The variance of X is equal to 16, and the variance of Y is equal to 9. Let Z = X -Y. What is the standard deviation of Z?
5.00
A sample of production records for an automobile manufacturer shows the following figures for production per shift: 705, 700, 690, 705. the variance of the sample is approximately
50.00
Suppose study participants are asked two questions. Based on a large number of participants, the probability distribution for the response to Question 1 and 2 is given below (check packet). For one participant, let A = Question 1 is answered correctly and B = Question 2 is answered correctly. Which of the following must be true?
A andB are not independent because (0.33)(0.45) does not equal 0.25
Why is the IQR considered to be a resistant statistic?
Adding a new extreme observation has little effect on it
Measurements of water quality were taken from a river downstream from an abandoned chemical dumpsite. Concentrations of a certain chemical were obtained from 9 measurements taken at the surface of the water, 9 measurements taken at mid-depth of the water, and 9 measurements taken at the bottom of the water. what type of study was conducted, and what is the response variable of the study?
An observational study was conducted, and the response variable is the concentration of the chemical
A random sample of golf scores gives the following summary statistics: n=20, x bar = 84.5, sx = 11.5, minX = 68, Q1 = 78, med = 86, Q3 = 91, maxX = 112. What can be said about the number of outliers?
At least 1
a linear regression was performed using the five following data points A(1, 11), B(5, 2), C(3, 7), D(7, 1), E(9, -2). The residual for which of the five points has the largest absolute value?
B
Given these parallel box plots, which of the following is incorrect?
Both sets are skewed to both lower and high values
The SC Electric Company has bid on two electrical wiring jobs. The owner of the company believes that: the probability of being awarded the first job (event A) is 0.17; the probability of being awarded the second job (event B) is 0.5; the probability of being awarded both jobs (A and B) is 0.375. If the owner's beliefs are correct, which of the following statements must be true concerning event A and event B?
Event A and Event B are not mutually exclusive, and are independent
What are the categorical variables in your survey?
Everything but average annual income and family size
Which of the following is true about the areas described under the normal curve?
Fewer than one percent of the cases are located three standard deviations above or below the mean
Given that the median is 270 and the interquartile range is 20, which of the following statements is true?
Fifty percent of the data are greater than or equal to 270
Using the regression equation above, correctly interpret the slope (using the equation y = 2.4 - .2 x where x = streetlight per block and y = crimes per month)
For every additional streetlight per block, the predicted crimes per month decrease by 0.2
A study is conducted relating AP Statistics exam scores to the total number of study hours for the AP Statistics class put in by students during the academic year, and the correlation is found to be .6, which of the following is a true statement?
Higher exam scores tend to be associated with higher numbers of study hours
A materials engineer wishes to compare the durability of two different types of paving material. She has 40 different one-mile stretches of interstate highway that she's been authorized to repave for this study. She decides to carry out a matched pairs experiment. Which of the following is the best way for her to carry out the randomization for this study?
Let each of the 40 roadways act as its own part, dividing each roadway into the first half-mile stretch and the second half-mile. Flip a coin for each of the 40 roadways to decide which half-mile gets which pavement
Which of the following can outliers affect significantly?
Mean, Standard Deviation, and Range
Which of the variables you collect are continuous data?
Only average annual income
Events D and E are independent, with P(D) = 0.6 and P(D and E) = 0.18. Which of the following is true?
P(D or E) = 0.72
Over the years, the size of houses in the unties states, based on the square footage of the house, has consistently increased. The data below represent a random selection of houses built during the years 1985 to 2004 (check packet). What is the least squares regression line for the information above?
Size = -45713 + 23.983(year)
Which of the following random variables has a distribution which most closely resembles a normal distribution?
The actual weight of a jar of peanut butter labeled as 16 ounces
As pat of a bear population study, data were gathered on a sample of black bears in the western United States to examine the relationship between the bears neck girth (distance around the neck) and the weight of the bear. below is some of the output from a least squares regression analysis examining the linear relationship between neck girth and weight. Which of the following is the correct value and corresponding interpretation for the correlation coefficient?
The correlation coefficient is 0.967. There is a strong positive linear relationship between the bears neck girth and its weight
An airline recorded the number of on-time arrivals for a sample of 100 flights each day. The box plot below summarizes the records data for one year. Based on the box plot, which of the following statements must be true?
The difference between the median and the lower quartile for the number of on-time arrivals is less than 2
A scatterplot of students heights, in inches, versus corresponding arm span length, in inches, is shown below. One of the points in the graph is labeled A. If the point labeled A is removed, which of the following statements would be true?
The slope of the lest squares regression line increases and the correlation coefficient increases
Which of the following is a true statement about the correlation coefficient r?
The square of the correlation measures the proportion of the y-variance that is predictable from a knowledge of x
An AP Statistics teacher grades using z-scores. On the second major exam of the marking period, a student receives a grade with a z-score -1.3. What is the correct interpretation of this grade?
The student scored 1.3 standard deviations lower on the second exam than the class average on the second exam
Which of the following statements concerning residuals from a LSRL is true?
all of the above
An advantage to using surveys as opposed to experiments is that
surveys are generally cheaper to conduct
If the standard deviation of a set is 0, you can conclude
that all observations are the same value
Suppose the probability that a softball player gets a hit in any single at-bat is .300. Assuming that her chance of getting a hit on a particular time at bat is independent of her other at bats, what is the probability that she will not get a hit until her fourth time at bat in a game?
(.3)^1 (.7)^3
Assume X and Y are events in the same sample space. If P(X) = 0.30 and P(Y) = 0.75 then which of the following inequalities must be true?
(P X n Y) >/= 0.05 and P(X nY) </= 0.30
The probability that a child will have a problem with alcohol is .75 if at least one of the parents is an alcoholic and .05 if neither parent is an alcoholic. In a recent study of a large number of children, 5% of the children involved has at least one parent who is an alcoholic. If a child in this study has an alcohol problem, what is the probability that at least one of the parents of the child is an alcoholic?
0.4412
(check packet for table) If P(A) = 0.25 and P(B) = 0.34, what is P(A U B) if A and B are independent?
0.505
People with type O-negative blood are universal donors. That is, any patient can receive a transfusion of O-negative blood. Only 7.2% of the American population has O-negative blood. If 10 people appear at random to give blood, what is the probability that at least 1 of them is a universal donor?
0.526
Calculate the residual for a block with 10 streetlights and 1 crime a month (using the equation y = 2.4 - .2 x where x = streetlight per block and y = crimes per month)
0.6
(check packet for table) Find the probability of a randomly drawn marble being large, given that the marble is black.
0.65
The average noise level in a bar is 36 decibels with a standard deviation of 5 decibels. Assuming a normal distribution, what is the probability the noise level is between 30 and 40 decibels?
0.673
The number of adults living in homes on a randomly selected city block is described by the following probability distribution (check packet). What is the standard deviation of the probability distribution?
0.89
It is estimated that 20 percent of all diver do not signal when changing lanes. in a random sample of four drivers, what is the probability that at least one doesn't signal when changing lanes?
1-(.8) ^4
How many crimes a month are predicted when there are 7 streetlights on a block? (using the equation y = 2.4 - .2 x where x = streetlight per block and y = crimes per month)
1.0
Given a set of ordered pairs (x, y) so that sx=0.75, sy=1.6, r=0.55. What is the slope of the least-squares regression line for these data?
1.17
A national achievement test is administered annually to 3rd graders. The test has a mean score of 100 and a standard deviation of 15. If Jane's z-score is 1.20, what was her score on the test
118
A researcher interested in the age at which women have their first child surveyed a simple random sample of 250 women who have one child and found an approximately normal distribution with a mean age of 27.3 and a star deviation of 5.4, According to the 68-95-99.7 rule, approximately 95% of women had their first child between the ages of
16.5 and 38.1
(A population of bolts has a mean thickness of 20 millimeters, with a population standard deviation of 0.01) Given, in millimeters, a minimum and maximum thickness that will include 95% of the population if bolts.
19.98 to 20.02 millimeters
(A population of bolts has a mean thickness of 20 millimeters, with a population standard deviation of 0.01) Given, in millimeters, a minimum and maximum thickness that includes 68% of the population of bolts
19.99 to 20.01 millimeters
To the nearest whole number, what percentile is associated with z = -0.68?
25th percentile
The following numbers appear in a table of random digits (check packet). A scientist will be measuring the total amount of leaf litter in a random sample (n=5) of forest sites selected without replacement from a population of 45 sites. The sites are labeled 01, 02, ... , 45 and she started at the beginning of the line of random digits and takes consecutive pairs of digits. Which of the following represents her sample?
38, 35, 02, 22, 40
Large bakery has many different products for sale. Suppose that 70% of all customers of the bakery order donuts, 50% order cinnamon rolls, and 40% order both. If a costumer is randomly selected, what is the probability that they order either donuts or cinnamon rolls, but not both?
40%
The scores on a real estate licensing examination given in a particular state are normally distributed with a stand deviation of 70. What is the mean test score if 25% of the applicants scored above 475?
428
In population H, what is the height, to the nearest tenth of an inch, of the 70th percentile?
67.3 inches
The weight of newborn baby boys have an approximately normal distribution with a mean of 8.0 pounds and a standard deviation of 1.5 pounds. A doctor tells a mother that her newborn baby boy has a weight at the 25th percentile. Which of the following is closest to this baby's weight?
7.00 pounds
Research indicates that the standard deviation of typical body temperature is0.4 degrees Celsius (C). Which of the following represents the standard deviation of typical human body temperature is degrees Fahrenheit (F), when F = 9/5 C + 32
9/5(0.4)
The dot plot below displays the daily high temperature, in degrees Fahrenheit, for a city in the southeastern United States during the 28 days in the month of February 2014 (check packet). Which of the following is closest to the percentile rank of a day in that month where the daily high temperature in this city was 70 degrees Fahrenheit?
95
In a statistics course, a linear regression equation was computed to predict the final exam score from the score on the first test. The equation was y = 10 + .9x where y is the final exam score and x is the score on the first test. Carla scored 95 on the first test. What is the predicted value of her score on the final exam?
95.5
Suppose that 30 percent of the subscribers to a cable television service watch the shopping channel at least once a week. You are to design a simulation to estimate the probability that none of five randomly selected subscribers watches the shopping channel at least once a week. which of the following assignments of the digits 0 through 9 would be appropriate for modeling an individual subscriber's behavior in this simulation?
Assign 0, 1, 2 as watching the shopping channel at least once a week and 3, 4, 5, 6, 7, 8, 9 as not watching
Halle takes three standardized tests. She scores 600on all three. Using standard scores (z-scores), rank her performance on the three tests from best to worst (check packet for table).
III, I, and II
Which of the following statements is true for two events, each with probability greater than 0?
If the events are mutually exclusive, they cannot be independent
A company wishes to survey what their customers think about a new product it plans to market. They decide to randomly sample from their customer database as this includes phone numbers and addresses. This procedure is an example of which type of sample?
Simple random
A scientist recorded the duration of the eruption of the Old Faithful geyser in Yellowstone National Park that occurred during a one-month time period. The histogram below shows the distribution of the curation, in seconds, of the eruptions. Based on the histogram, which of the following is the best description of the distribution?
The distribution displays two clusters with one cluster centered at about 125 seconds and the other centered at about 260 seconds, and has a range of at most 250 seconds.
A set of data has a mean that is much larger than the media. Which of the following statements is most consistent with this information?
The distribution is skewed right
Ms. Fisher wanted to compare the effect of a new fertilizer on that of three older fertilizers - X, Y, and Z - on the growth of vegetables typically grown in small gardens. 200 green bean seedlings were individually planted in identical pots and randomly assigned to one of four groups of 50 each...the scientists concluded that the new fertilizer was more effective than the other fertilizers for all vegetables. Why is Ms. Fisher's conclusion not appropriate?
The experiment only included green beams, so the results cannot be generalized to all vegetables
A set of data relates the amount of annual salary raise and the performance rating. The least squares regression equation is y hat = 2000 x + 1400 where y is the estimated raise and x is the performance rating. Which of the following statements is not correct?
This equation produces predicted raises with an average error of 0
The faces of a four-sided die are numbered 1 through 4 respectively. for a certain game, the die is tossed and the number that lands facedown is recorded. (Check packet for table) Consider two independent tosses of the die. Let the random variable S represent the sum of the points earned from the two cases. Which table represents the probability distribution of S?
Top row: 0, 1, 2, 3, 4, bottom row: 0.25, 0.25, 0.3125, 0.125, 0.0625
Which of the following are true?
Two events are mutually exclusive if they can't both occur at the same time; an event and its implement have probabilities that always add to 1
Which of the following statements is incorrect?
Voluntary response samples often underrepresent people with strong opinions
A study was conducted to evaluate the impact of taking a nutritional supplement on a person's reaction time. One hundred volunteers were places into one of three groups according to their athletic ability: low, moderate, or high. Participants in each group were randomly assigned to take either the nutritional supplement or a placebo for six weeks. At the end of the weeks, participants were given a coordination task. The reaction time in completing the task was recorded for each participant. The study compared the reaction times between those taking the supplement and those taking the placebo within each athletic ability level. Which of the following is the best description of the study?
a randomized block design
A critical difference between experiments and observational studies is
an experiment often suggests a causal relationship, whereas an observational study only suggests an association
Rainwater was collected in water collectors at 30 different sites near na industrials complex and the amount of acidity (pH level) was measured. The data ranged from pH 2.6 to pH 6.3. (check packet for stemplot) Which of the following box plots is a correct representation of the same distribution?
center of 4.5, range from 2.6 to 6.4
control groups are used in experiments in order to
control the effects of lurking variables such as the placebo effect
A national consumer magazine reported the following correlation: The correlation between car weight and car reliability is -0.30. The correlation between car weight and annual maintenance cost is 0.20. Which of the following statements are true>
heavier cars tend to be less reliable; heavier cars tend to cost more to maintain; car weight is related more strongly to reliability than to maintenance cost (all of them are true)
Given two events, E and F, such that P(E) = .340, P(F) = .450, and P(E U F) = .637, then the two events are:
independent, but not mutually exclusive
A residual:
is how much an observed y-value differs from predicted y-value
When drawing histograms it is important to
label the vertical axis so the reader can determine the counts or percents in each class interval
In which of the following histograms is the mean less than the median?
looks like a staircase with the right side higher and the left side lower
100 volunteers who suffer from anxiety take part in a study. 50 are selected at random and assigned to receive a new drug that is thought to be extremely effective in reducing anxiety. The other 50 are given an existing anti-anxiety drug. A doctor evaluates anxiety levels after two month go treatment to determine if there has been a larger reduction in the anxiety levels of those who take the new drug. This would be double blind if
neither the subjects nor the doctor knew which treatment any subject had received
The back-to-back stemplot on the right shows the number of books read in year by a random sample of college and high school students. Which of the following statements are true?
one college student read seven books; the college median is equal to the high school median; the mean is greater than the median in both groups; (all of them are true)
Lauren is enrolled in a very large college calculus class. On the first exam, the class mean was 75 and the standard deviation was 10. On the second exam, the class mean was 70 and the standard deviation was 15. Lauren scored 85 on both exams. Assuming the scores on each exam were approximately normally distributed, on which exam did Lauren score better relative to the rest of the class?
she scored about equally well on both exams
A bank wishes to survey its costumers. The decision is made to randomly pick ten costumes who just have checking accounts, ten costumers who just have savings accounts, and ten customers who have both checking and savings accounts. This procedure is an example of which type of sampling?
stratified
which of the following are true statements?
the area under a normal curve is always equal to 1, no matter what the mean and standard deviation are; the smaller the standard deviation of a normal curve, the higher and narrower the graph; normal curves with different means are centered around different number; (all of them are true)
Which of the following is correct
the coefficient of determination is the fraction of variability in y that can be explained by least-squares regression of y on x
The effect of removing the right-most point (near positive x-axis) in the scatterplot shown would be
the sloe of the LSRL will increase, r will increase
Given two independent random variables, X with mean 12.3 and standard deviation 0.5 and Y with mean 9.1 and standard deviation 0.3, which of the following is a true statement?
the variance of X - Y is 0.34
Two antidepressants are to be compared in the treatment of elderly patients in a nursing home. Each patient has his or her own room, some with spectacular views of the oceans. The experimental design is to create homogenous blocks with respect to window view. How should randomization be used for a randomized block design?
within each block, randomly pick half the patients to receive each antidepressant
In population H, what is the z-score, to the nearest tenth, associated with the height 65 inches?
z = -0.4