AP Stats final

The distribution of assembly times required to assemble a certain smartphone is approximately normal with mean 4.6 minutes and standard deviation 0.6 minute. Of the following, which is closest to the percentage of assembly times between 4 minutes and 5 minutes?

59%

The table shows several values of xx and their corresponding values of y. Which of the following is closest to the correlation between x and y?

0.98

The caffeine content of 8-ounce cans of a certain cola drink is approximately normally distributed with mean 33 milligrams (mg). A randomly selected 8-ounce can containing 35 mg of caffeine is 1.2 standard deviations above the mean. Approximately what percent of 8-ounce cans of the cola have a caffeine content greater than 35 mg?

12%

Approximately what percent of the participants had finishing times greater than Shalise's for each puzzle?

16% on the small puzzle and 84% on the large puzzle

Which of the following is closest to the percentile rank of a resident from this street who traveled 85 miles to work that week?

80

A study was conducted to evaluate the impact of taking a nutritional supplement on a person's reaction time. One hundred volunteers were placed 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 six 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

At a certain clothing store, the clothes are displayed on racks. The clothes on each rack have similar prices, but the prices among the racks are very different. To estimate the typical price of a single piece of clothing, a consumer will randomly select four pieces of clothing from each rack. What type of sample is the consumer selecting?

A stratified random sample

Janelle collected data on the amount of time in minutes each person in a large sample of customers spent in a local store. The data also included recording the gender of each customer. These data were used to generate the boxplots shown below.

Approximately half of the males in the sample of customers spent at least as much time in the store as any female in the sample of customers.

Data were collected on the amount, in dollars, that individual customers spent on dinner in an Italian restaurant. The quartiles for these data are given below.

At least half of the customers spent less than or equal to $44.27 and at least half spent greater than or equal to $44.27.

At a large airport, data were recorded for one month on how many baggage items were unloaded from each flight upon arrival as well as the time required to deliver all the baggage items on the flight to the baggage claim area. A scatterplot of the two variables indicated a strong, positive linear association between the variables. Which of the following statements is a correct interpretation of the word "strong" in the description of the association?

B

Some people claim the procedure being used does not permit the results to be extended to all registered voters. Which of the following is NOT a legitimate concern about the procedure being used?

B

Which of the following could be the median of the waiting times, in minutes?

B. 7.25

Athletes in a particular sport are classified as either offense or defense. The distribution of weights for the athletes classified as offense is approximately normal, centered at 200 pounds, and ranges from 150 pounds to 250 pounds. The distribution of weights for the athletes classified as defense is approximately normal, centered at 300 pounds, and ranges from 250 pounds to 350 pounds. There are 1,000 athletes in each classification. Which of the following is the best description of a histogram of the weights of all 2,000 athletes?

Bimodal

One point is circled on graph 11. Five points labeled A, B, C, D, and E are identified on graph 22. Which point on graph 22 represents the residual for the circled point on graph 11 ?

C

A produce supplier ships boxes of produce to individual customers. The distribution of weights of shipped boxes is approximately normal with mean 36 pounds and standard deviation 4 pounds. Which expression represents the weight, in pounds, at the 75th percentile of the distribution?

D

The distribution of heights of 6-year-old girls is approximately normally distributed with a mean of 46.0 inches and a standard deviation of 2.7 inches. Aliyaah is 6 years old, and her height is 0.96 standard deviation above the mean. Her friend Jayne is also 6 years old and is at the 93rd percentile of the height distribution. At what percentile is Aliyaah's height, and how does her height compare to Jayne's height?

D

The distribution of the weights of loaves of bread from a certain bakery follows approximately a normal distribution. Based on a very large sample, it was found that 10 percent of the loaves weighed less than 15.34 ounces, and 20 percent of the loaves weighed more than 16.31 ounces. What are the mean and standard deviation of the distribution of the weights of the loaves of bread?

D

An outlier may be defined as a data point that is more than 1.5 times the interquartile range below the lower quartile or is more than 1.5 times the interquartile range above the upper quartile. According to this definition, what is the diameter, in inches, of the smallest tree that is an outlier?

D. 34

A botanist found a correlation between the length of an aspen leaf and its surface area to be 0.94. Why does the correlation value of 0.94 not necessarily indicate that a linear model is the most appropriate model for the relationship between length of an aspen leaf and its surface area?

E

A sample of 100 students from Liberty High School and a sample of 60 students from Central High School were asked what they planned to do after graduation. Responses fell into five categories: four-year university (4Y)(4Y), community college (CC)(CC), join the workforce (W)(W), join the military (M)(M), or undecided (UD)(UD). The results are shown in the following bar chart.

For the category undecided, the number of students from Liberty High School was 4 greater than the number of students from Central High School.

Which of the following indicates an association between the shooter's choice of direction and the goalie's choice of direction?

For the goalie, the relative frequency of a direction is not equal to the relative frequency conditioned on the shooter's direction.

Which statement gives the best comparison between the number of defective parts produced by the machines during the first hour of operation on the 19 days?

Machine A usually, but not always, produced fewer defective parts than machine B.

A company wanted to determine the health care costs of its employees. A sample of 25 employees were interviewed and their medical expenses for the previous year were determined. Later the company discovered that the highest medical expense in the sample was mistakenly recorded as 10 times the actual amount. However, after correcting the error, the corrected amount was still greater than or equal to any other medical expense in the sample. Which of the following sample statistics must have remained the same after the correction was made?

Median

Roger claims that the two statistics most likely to change greatly when an outlier is added to a small data set are the mean and the median. Is Roger's claim correct?

No, only the mean is likely to change greatly.

A certain motel is roughly 20 miles from the entrance to Yosemite National Park. The motel manager wants to get a better estimate of the distance and asks five people to each measure the distance, to the nearest tenth of a mile, using the odometer in his or her car. The manager will use the median of the five measurements as the estimate of the distance. Which of the following statements is NOT a statistical justification for the manager's plan?

The actual distance should be considered a variable, and taking five measurements allows the manager to estimate the variability in the actual distance.

In northwest Pennsylvania, a zoologist recorded the ages, in months, of 55 bears and whether each bear was male or female. The data are shown in the back-to-back stemplot below.

The median age and the range of ages are both greater for female bears than for male bears.

One way to measure the duration of subterranean disturbances such as earthquakes and mining is to calculate the root-mean-square time. The following histograms summarize the distributions of the root-mean-square times for two sources of disturbances.

The median of the earthquake disturbances is less than the median of the mining disturbances.

The prices, in thousands of dollars, of 304 homes recently sold in a city are summarized in the histogram below.

The median price is not greater than $750,000.

The following bar chart displays the relative frequency of responses of students, by grade level, when asked, "Do you volunteer in a community-service activity?"

The number of tenth-grade students who responded yes was greater than the number of ninth-grade students who responded yes.

If the interval size is decreased from $200 to $100, which of the following must remain the same on the new histogram?

The sum of the frequencies

A restaurant manager collected data on the number of customers in a party in the restaurant and the time elapsed until the party left the restaurant. The manager computed a correlation of 0.78 between the two variables. What information does the correlation provide about the relationship between the number of customers in a party at the restaurant and the time elapsed until the party left the restaurant?

c

pounds?

no

Students in a large psychology class measured the time, in seconds, it took each of them to perform a certain task. The times were later converted to minutes. If a student had a standardized score of z = 1.72 before the conversion, what is the standardized score for the student after the conversion?

z = 1.72

For a random sample of 20 professional athletes, there is a strong, linear relationship between the number of hours they exercise per week and their resting heart rate. For the athletes in the sample, those who exercise more hours per week tend to have lower resting heart rates than those who exercise less. Which of the following is a reasonable value for the correlation between the number of hours athletes exercise per week and their resting heart rate?

−0.87

The height and age of each child in a random sample of children was recorded. The value of the correlation coefficient between height and age for the children in the sample was 0.80.8. Based on the least-squares regression line created from the data to predict the height of a child based on age, which of the following is a correct statement?

The proportion of the variation in height that is explained by a regression on age is 0.640.64.

A data set of test scores is being transformed by applying the following rule to each of the raw scores. Transformed score = 3.5(raw score) + 6.2 Which of the following is NOT true?

The range of the transformed scores equals 3.5(the range of the raw scores) + 6.2.

The histogram shows the distribution of heights, in inches, of 100 adult men. Based on the histogram, which of the following is closest to the interquartile range, in inches, of the distribution?

5

A researcher is studying a group of field mice. The distribution of the weight of field mice is approximately normal with mean 25 grams and standard deviation 4 grams. Which of the following is closest to the proportion of field mice with a weight greater than 33 grams?

0.023

The commuting time for a student to travel from home to a college campus is normally distributed with a mean of 30 minutes and a standard deviation of 5 minutes. If the student leaves home at 8:25 A.M., what is the probability that the student will arrive at the college campus later than 9 A.M.?

0.16

At a small coffee shop, the distribution of the number of seconds it takes for a cashier to process an order is approximately normal with mean 276 seconds and standard deviation 38 seconds. Which of the following is closest to the proportion of orders that are processed in less than 240 seconds?

0.17

A random sample of 1,0921,092 people were asked whether color was a consideration in buying a new car. They were also asked to identify one additional feature that was important. The responses are shown in the table.

0.18

Scientists working for a water district measure the water level in a lake each day. The daily water level in the lake varies due to weather conditions and other factors. The daily water level has a distribution that is approximately normal with mean water level of 84.07 feet. The probability that the daily water level in the lake is at least 100 feet is 0.064. Which of the following is closest to the probability that on a randomly selected day the water level in the lake will be at least 90 feet?

0.29

Suppose a certain scale is not calibrated correctly, and as a result, the mass of any object is displayed as 0.75 kilogram less than its actual mass. What is the correlation between the actual masses of a set of objects and the respective masses of the same set of objects displayed by the scale?

1

The distribution of monthly rent for one-bedroom apartments in a city is approximately normal with mean $936 and standard deviation $61. A graduate student is looking for a one-bedroom apartment and wants to pay no more than $800 in monthly rent. Of the following, which is the best estimate of the percent of one-bedroom apartments in the city with a monthly rent of at most $800 ?

1.3%

A grocery store receives deliveries of corn from two farms, one in Iowa and the other in Ohio. Both farms produce ears of corn with mean weight 1.261.26 pounds. The standard deviation of the weights of the ears of corn from the farm in Ohio is 0.010.01 pound greater than that from the farm in Iowa. A randomly selected ear of corn from the farm in Iowa weighed 1.391.39 pounds, which has a standardized score of 1.6451.645 for the distribution of weights for the Iowa corn. If an ear of corn from the farm in Ohio weighs 1.391.39 pounds, how many standard deviations from the mean is the weight with respect to the Ohio distribution?

1.46 standard deviations above the mean

Scientists estimate that the distribution of the life span of the Galápagos Islands giant tortoise is approximately normal with mean 100100 years and standard deviation 1515 years. Based on the estimate, which of the following is closest to the age of a Galápagos Islands giant tortoise at the 90th90th percentile of the distribution?

120 years

For a certain online store, the distribution of number of purchases per hour is approximately normal with mean 1,200 purchases and standard deviation 200 purchases. For what proportion of hours will the number of purchases at the online store exceed 1,400 ?

16%

A sleep time of 15.9 hours per day for a newborn baby is at the 10th percentile of the distribution of sleep times for all newborn babies. Assuming the distribution is normal with standard deviation 0.5 hour, approximately what is the mean sleep time, in hours per day, for newborn babies?

16.5

A statistician at a metal manufacturing plant is sampling the thickness of metal plates. If an outlier occurs within a particular sample, the statistician must check the configuration of the machine. The distribution of metal thickness has mean 23.5 millimeters (mm)(mm) and standard deviation 1.4 mmmm. Based on the two-standard deviations rule for outliers, of the following, which is the greatest thickness that would require the statistician to check the configuration of the machine?

20.6mm

The number of hurricanes reaching the East Coast of the United States was recorded for each of the last ten decades by the National Hurricane Center. Summary measures are shown below.

24 is an outlier and it is possible that there are other outliers at the high end of the data set. There are no outliers at the low end of the data set.

At a certain store, the distribution of weights of cartons of large eggs is approximately normal with mean 26 ounces (oz). Based on the distribution, which of the following intervals will contain the greatest proportion of cartons of large eggs at the store?

24 oz to 28 oz

The distribution of lengths of salmon from a certain river is approximately normal with standard deviation 3.5 inches. If 10 percent of salmon are longer than 30 inches, which of the following is closest to the mean of the distribution?

28 inches

Which of the following values represents the predicted change in the height of the tree for each one-meter increase in the diameter of the tree?

30

The height of 3-year-old boys is approximately normally distributed. Duncan and Shane are 3-year-old boys.Duncan is 32.0 inches tall and is at the 32nd percentile of the distribution. Shane is 34.0 inches tall and is at the 62nd percentile of the distribution. Which of the following is closest to the mean of the height distribution?

33.21 inches

Based on the boxplot, the top 25 percent of the cars have a typical gas mileage of at least how many miles per gallon?

35

For a recent season in college football, the total number of rushing yards for that season is recorded for each running back. The mean number of rushing yards for the running backs that season is 790 yards. One running back had 1,637 rushing yards for the season, which is 2.42 standard deviations above the mean number of rushing yards. What is the standard deviation of the number of rushing yards for the running backs that season?

350 yards

Each value in a sample has been transformed by multiplying by 3 and then adding 10. If the original sample had a variance of 4, what is the variance of the transformed sample?

36

What value of a would indicate no association between gender and voting pattern for the people in the sample?

480

The heights of adult women are approximately normally distributed about a mean of 65 inches with a standard deviation of 2 inches. If Rachael is at the 99th percentile in height for adult women, then her height, in inches, is closest to

70

A candy company produces individually wrapped candies. The quality control manager for the company believes that the weight of the candies is approximately normally distributed with mean 720 milligrams (mg).If the manager's belief is correct, which of the following intervals of weights will contain the largest proportion of the candies in the distribution of weights? A

700 mg to 740 mg

Some descriptive statistics for a set of test scores are shown above. For this test, a certain student has a standardized score of z = -1.2. What score did this student receive on the test?

779.42

Research indicates that the standard deviation of typical human body temperature is 0.4 degree Celsius (C). Which of the following represents the standard deviation of typical human body temperature in degrees Fahrenheit (F), where

9/5(0.4)

A market research firm is studying the effects of price and type of packaging on sales of a particular product. Twenty-seven stores with shoppers of similar characteristics will be used in the study. The nine combinations of three price levels and three packaging types are the treatments of interest. Total sales of the product over a seven-week period will be recorded. Which of the following describes the best design to use for the study?

A

Suppose a roadrunner has a total length of 59.0 cm and tail length of 31.1 cm. Based on the residual, does the regression model overestimate or underestimate the tail length of the roadrunner?

A

In a recent survey, high school students and their parents were asked to rate 60 recently released movies. The ratings were on a scale from 1 to 9, where 1 was "horrible" and 9 was "excellent". For each movie, the average rating by the students and the average rating by their parents was calculated and the scatterplot below was constructed.The horizontal axis represents the student rating, and the vertical axis represents the parent rating.Thus, an individual data point would represent the rating of a single movie.

B

As part of a study on facility needs, the administrators of a university wanted to estimate the percent of students who use the exercise facilities on a regular basis. From the 34,000 students who attend the university, a random sample of 370 male students and 400 female students was selected. Of the 770 students selected, 493 students indicated that they use the exercise facilities on a regular basis. What are the population and the sample of the study?

D

In a certain school district, students from grade 6 through grade 12 can participate in a school-sponsored community service activity. The following bar chart shows the relative frequencies of students from each grade who participate in the community service activity.

Grade 12 had the least relative frequency of participating students.

A local television news station includes a viewer survey question about a current issue at the beginning of every evening news broadcast. Viewers are invited to use social media to respond to the question. The results of the survey are shared with the audience at the end of each broadcast. In relation to the opinions of the population of the region, which of the following is a possible reason why the results of such surveys could be biased?

I, II and III

The values 60, 62, and 84 were common to both samples. The three values are identified as outliers with respect to the age-group 20 years to 3030 years because they are either 1.5 times the interquartile range (IQR)greater than the upper quartile or 1.5 times the IQR less than the lower quartile. Using the same method for identifying outliers, which of the three values are identified as outliers for the age-group 40 years to 50years?

Only 6060 is identified as an outlier.

In a recent poll of 1,500 randomly selected eligible voters, only 525 (35 percent) said that they did not vote in the last election. However, a vote count showed that 80 percent of eligible voters actually did not vote in the last election. Which of the following types of bias is most likely to have occurred in the poll?

Response bias

The height hh and collar size cc, both in centimeters, measured from a sample of boys were used to create the regression line cˆ=−94+0.9hc^=−94+0.9h. The line is used to predict collar size from height, both in centimeters, for boys' shirt collars. Which of the following has no logical interpretation in context?

The c-intercept of the regression line

For a sample of 42 rabbits, the mean weight is 5 pounds and the standard deviation of weights is 3 pounds. Which of the following is most likely true about the weights for the rabbits in this sample?

The distribution of weights is skewed to the right because the least possible weight is within 2 standard deviations of the mean.

Nutritionists examined the sodium content of different brands of potato chips. Each brand was classified as either healthy or regular based on how the chips were marketed to the public. The sodium contents, in milligrams (mg) per serving, of the chips are summarized in the boxplots below.

The interquartile range (IQR) of the brands classified as healthy is greater than the IQR of the brands classified as regular.

If the point labeled A is removed, which of the following statements would be true?

The slope of the least squares regression line increases and the correlation coefficient increases.

Which of the following statements must be true about the data sets A and B displayed in the histograms above?

The standard deviation of data set A is greater than the standard deviation of data set B.

As part of a science experiment, a student recorded 10 measurements of the temperature of a liquid. One of the measurements was an outlier when compared with the other 9 measurements. Which of the following must be true about the 9 measurements, excluding the outlier, when compared with the 10 measurements?

The standard deviation of the 9 measurements is less than the standard deviation of the 10 measurements.

Nyasha's financial literacy project involved comparing the annual sales of companies in Canada and companies in the United States that produce software. Using the ratio of 1 Canadian dollar to 0.75 United States dollar, she converted all annual sales from the Canadian companies into United States dollars. For which of the following will the value of the statistic for the annual sales in Canadian dollars be equal to the value of the corresponding statistic in United States dollars?

The standardized score of the minimum annual sales

A graph (not shown) of the selling prices of homes in a certain city for the month of April reveals that the distribution is skewed to the left. Which of the following statements is the most reasonable conclusion about the selling prices based on the graph?

The value of maximum minus third quartile is less than the value of first quartile minus minimum.

The data were used to fit a least-squares regression line to predict the number of hours of pain relief for a given dose. Which of the following would be revealed by a plot of the residuals of the regression versus the dose?

The variation in the hours of pain relief is not the same across the doses.

A survey of 57 students was conducted to determine whether or not they held jobs outside of school. The two-way table above shows the number of students by employment status (job, no job), and class (juniors, seniors). Which of the following best describes the relationship between employment status and class?

There appears to be an association, since the proportion of juniors having jobs is much larger than the proportion of seniors having jobs.

At a photography contest, entries are scored on a scale from 1 to 100. At a recent contest with 1,000 entries, a score of 68 was at the 77th percentile of the distribution of all the scores. Which of the following is the best description of the 77th percentile of the distribution?

There were 770 entries with a score less than or equal to 68.

To compare the effectiveness of two treatments, researchers conducted a well-designed experiment using a randomized block design in which the subjects were blocked by age-group (under 4040 years and 4040 years or older). Which of the following must be true about the randomized block design of the experiment?

Treatments are randomly assigned to subjects within each block.