KHAN AP STATS

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cars

-0.246 +- 3.25(0.013)

Arabella collected data about life expectancy (in years) and infant mortality (per \[1000\]) in a random sample of \[33\] countries. Here is computer output from a least-squares regression analysis on her sample: Assume that all conditions for inference have been met. Which of these is a \[90\%\] confidence interval for the slope of the least squares regression line?

-0.442 +- 1.7(0.037)

christine

-5 += 2.75(0.52)

Lennox had been scheduling employees based on the assumption that the following distribution represented when people made purchases in his store.

Which of these graphs does NOT show a valid probability distribution? Choose 1 answer:

Graph B or Graph A

The dot plot shows the weight, in pounds, of \[25\] students' filled backpacks. Each dot represents one backpack.

\[96^{\text{th}}\] percentile

The lifespans of lions in a particular zoo are normally distributed. The average lion lives \[10\] years; the standard deviation is \[1.4\] years. Use the empirical rule \[(68 - 95 - 99.7\%)\] to estimate the probability of a lion living longer than \[7.2\] years.

\[97.5\%\]

The distribution of annual profit at a chain of stores was approximately normal with mean \[\mu = \$66{,}000\] and standard deviation \[\sigma = \$21{,}000\]. The executives conducted an audit of the stores with the lowest \[20\%\] of profits. What is closest to the maximum annual profit at a store where the executives conducted an audit?

\[\$48{,}000\]

A set of average city temperatures in April are normally distributed with a mean of \[19.7 ^\circ \text{C}\] and a standard deviation of \[2 ^\circ \text{C}\]. The average temperature of Kabul is \[15 ^\circ \text{C}\]. What proportion of average city temperatures are lower than that of Kabul?You may round your answer to four decimal places.

\[\greenD{0.0094}\]

Nancy obtained a random sample of students and noticed a positive linear relationship between their ages and the amount of water (in \[\text{mL}\]) they said they drank yesterday. A \[95\%\] confidence interval for the slope of the regression line was \[(16.3, 154.8)\]. Nancy wants to use this interval to test \[\text{H}_0\text{: } \beta=0\] vs. \[\text{H}_\text{a}\text{: } \beta\neq 0\] at the \[\alpha=0.05\] level of significance. Assume that all conditions for inference have been met.

leonard

An educational psychologist wondered whether there was a relationship between the amount of academic pressure a high school student felt and their plans for college. They surveyed a random sample of \[300\] high school students throughout the country about their college plans and whether they felt academic pressure. Here are the responses and partial results of a chi-square test (expected counts appear below observed counts):

Whitney's town has \[10{,}000\] residents and three neighborhoods. These are the percentages of each neighborhood's area relative to the town's total area:

first 3

peter

first 3

The distribution of raw scores on a particular achievement test has a mean of \[500\] and a standard deviation of \[80\]. If each score is increased by \[25\], what will be the mean and standard deviation of the distribution of new scores?

mean 525 sd 80

Kenji runs a channel where he uploads and shares videos that he makes. He noticed an exponential relationship between how long his videos have been posted and the number of times each video has been viewed.

265

sebastian

\[-1.133\pm 2.365(0.27)\]

Cora is playing a game that involves flipping three coins at once. Let the random variable \[H\] be the number of coins that land showing "heads". Here is the probability distribution for \[H\]:

\[P(H<3)=0.875\]

Adele read an article about how tax-payers completed the majority of their tax forms. Here is what the article stated:

In one county, the farms had a mean harvested area of \[103\] acres with a standard deviation of \[9\] acres. What will be the mean and standard deviation of the distribution of area in square kilometers?\[1\] acre approximately equals \[0.004\] square kilometers.

mean 0.412 sk sd 0.036 sk

ona

14.02 +- 2.878(1.15)

Margot surveyed a random sample of \[180\] people from the United States about their favorite sports to watch. Then she sent separate, similar, survey to a random sample of \[180\] people from the United Kingdom. Here are the results:

The amount of cleaning solution a company fills its bottles with has a mean of \[33\,\text{fl oz}\] and a standard deviation of \[1.5\,\text{fl oz}\]. The company advertises that these bottles have \[32\,\text{fl oz}\] of cleaning solution. What will be the mean and standard deviation of the distribution of excess cleaning solution, in milliliters?\[(1\,\text{fl oz}\] is approximately \[30\,\text{mL}.)\]

30 45

Patrick is a health researcher. He wonders if emergency room visits are evenly distributed across the days of the week. He plans to take a random sample of recent visits in order to carry out a \[\chi^2\] goodness-of-fit test on the results. What is the smallest sample size Patrick can take to pass the large counts condition?

The distribution of durations for which apartments remain empty after the resident moves out for one property management company over the past \[10\] years was approximately normal with mean \[\mu = 85\] days and standard deviation \[\sigma = 29\] days. The property management company tags the files of the apartments that were empty for the shortest \[5\%\] of durations to have priority cleaning the next time their residents move out.

Jonas runs a channel where he uploads and shares videos that he makes. He noticed an exponential relationship between how long his videos have been posted and the number of times each video has been viewed.

The distribution of resting pulse rates of all students at Santa Maria high school was approximately normal with mean \[\mu = 80\] beats per minute and standard deviation \[\sigma = 9\] beats per minute. The school nurse plans to provide additional screening to students whose resting pulse rates are in the top \[30\%\] of the students who were tested.

Elisabeth has a collection of "liked" songs on her phone. She has her phone set to play one of these songs as her alarm every morning. Here is a summary of the genres of these songs: Which graph correctly displays the probability distribution for the genre of a song on a given morning?

A company plans on offering a new smartphone in four colors: black, white, silver, and gold. They suspect that \[55\%\] of customers prefer black, \[20\%\] prefer white, \[10\%\] prefer silver, and \[15\%\] prefer gold. They take a random sample of \[33\] potential customers to see what color they prefer. Here are the results:

D + E

Paula runs every morning. She tracked the temperature (in degrees Celsius) and how far she ran (in kilometers) for a random sample of runs. She saw a negative relationship between the temperatures and distances. A \[95\%\] confidence interval for the slope of the regression line was \[(-0.02, 0.12)\]. Paula wants to use this interval to test \[\text{H}_0\text{: } \beta=0\] vs. \[\text{H}_\text{a}\text{: } \beta\neq 0\] at the \[\alpha=0.05\] level of significance. Assume that all conditions for inference have

Fail to reject \[\text{H}_0\]. Paula can't conclude a linear relationship between temperature and distance.

Carley owns an ice cream stand. She wants to predict how many ice cream cones she will sell as a function of the average daily high temperature each month. The data for the past \[7\] months is shown in the table below.

Graph C

Leonard took a random sample of his recent text messages and found a positive linear relationship between how many minutes he took to reply and how many minutes the other person took to reply. Here is computer output from a least-squares regression analysis on his sample:

No, since \[0.168>0.05\].

Jermaine took a random sample of students at his school and measured the length of each student's index and ring finger on their right hand. He noticed a positive linear relationship between the lengths. Here is computer output from a least-squares regression analysis on his sample:

Reject \[\text{H}_0\]. This suggests a linear relationship between index and ring finger length.

The grades on a math midterm at Loyola are roughly symmetric with \[\mu = 68\] and \[\sigma = 5.5\]. Jessica scored \[66\] on the exam.

\[-0.36\]

Yuki weighed several soil samples, each filling a quarter liter measuring cup. The distribution of masses has a mean of \[215\,\text{g}\] and a standard deviation of \[60\,\text{g}\]. After recording her measurements, Yuki realized that she had forgotten to subtract the mass of the measuring cup, which is \[20\,\text{g}\]. What will be the mean and standard deviation of the distribution of corrected measurements?

mean 195g sd 60g

Eitan sells a mean of \[\$8000\] worth of merchandise with a standard deviation of \[\$1500\] each month. Each month, Eitan earns a base salary of \[\$2000\] plus a commission of \[30\%\] of his sales. He calculates his total salary according to this formula: \[\text{[total salary]}=\text{commission}+\text{[base salary]}\] What will be the mean and standard deviation of the distribution of Eitan's total monthly salary? Choose 1 answer:

mean 4400 sd 450 dollars

The cargo loads that Niels transports in his truck have a mean weight of \[42{,}000\,\text{lb}\] with a standard deviation of \[1{,}500\,\text{lb}\]. What will be the mean and standard deviation of the distribution of weights in kilograms?\[1\,\text{lb}\] approximately equals \[0.45\,\text{kg}\].

mean: 18900 kg sd 657 kg

The American Community Survey is completed by the US Census Bureau to obtain information about households in the US. One variable of interest is how many people reside in each household (vacant households were recorded as having zero people). Based on data from 2014, here is the partially completed probability distribution of \[H\], the number of people residing in a randomly selected US household: \[P\left(H=0\right)=\]

0.12

Mr. Dennis gave his class a \[20\]-question multiple choice quiz. The distribution of raw scores had a mean of \[15\] and a standard deviation of \[2.5\]. Mr. Dennis is going to multiply each raw score by \[5\] so the quiz is worth a total of \[100\] points. If each score is multiplied by \[5\], what will be the mean and standard deviation of the distribution of new scores?

75 12.5

According to the distributor of a kind of trading card, \[66\%\] of the cards are common, \[25\%\] are uncommon, and \[9\%\] are rare. Pin-Yen wondered if the rarity levels of the cards she and her friends owned followed this distribution, so she took a random sample of \[500\] cards and recorded their rarity levels. Here are her results:

Daphne likes to ski at a resort that is open from December through April. According to a sign at the resort, \[20\%\] of the snowfalls occur in December, \[25\%\] in January, \[20\%\] in February, \[20\%\] in March, and \[15\%\] in April. She wondered if the snowfalls in her hometown followed this distribution, so she took a random sample of \[80\] days between December and April with snowfall and recorded their months. Here are her results:

Joe wondered whether the days of the week of health clinic appointments at his clinic had an even distribution from Monday through Friday, so he took a random sample of \[500\] health clinic appointments and recorded their days of the week. Here are his results: DayMondayTuesdayWednesdayThursdayFridayAppointments\[115\]\[100\]\[115\]\[100\]\[70\]

Alicia took a random sample of mobile phones and found a positive linear relationship between their processor speeds and their prices. Here is computer output from a least-squares regression analysis on her sample:

Yes, since \[0.002<0.01\].

A random sample of internet subscribers from the west coast of the United States was asked if they were satisfied with their internet speeds. A separate random sample of adults from the east coast was asked the same question. Here are the results:

\[19.2\]

\[P(X \geq 2)=0.8\]

Hugo plans to buy packs of baseball cards until he gets the card of his favorite player, but he only has enough money to buy at most \[4\] packs. Suppose that each pack has probability \[0.2\] of containing the card Hugo is hoping for. Let the random variable \[X\] be the number of packs of cards Hugo buys. Here is the probability distribution for \[X\]: What is the probability that Hugo buys fewer than \[3\] packs of cards? \[P(\text{fewer than }3 \text{ packs})=\]

0.36

Sophie wanted to know if sons of taller fathers tend to be taller. She collected data about the heights of a random sample of \[110\] men and about their fathers' heights. Here is computer output from a least-squares regression analysis on her sample: Assume that all conditions for inference have been met. Which of these is a \[90\%\] confidence interval for the slope of the least squares regression line?

0.431 +- 1.66(0.059)

0.64

A chain of stores knows that \[90\%\] of its customers pay with a credit or debit card, \[5\%\] pay with cash, and \[5\%\] pay with a service on their smartphones. They installed a new system for receiving payments, and they wonder if these percentages still hold true. They plan to take a random sample of customers in order to perform a \[\chi^2\] goodness-of-fit test on the results.

100

Tate works at an ice cream stand. Every customer can choose one of two toppings—sprinkles or chocolate chips. He recorded the age group and the chosen topping for a random sample of \[120\] customers. Here are the results:

A biologist studying spotted bass observed a quadratic relationship between the lengths and weights of fish in a large sample. The biologist took the base \[10\] logarithm for the values of both variables, and they noticed a linear relationship in the transformed data.

2.2

A panel of judges was asked to judge the quality of a random sample of \[24\] brands of potato chips. Here is computer output from a least-squares regression analysis on the relationship between the price of each brand (in dollars per pack) and its rating:

2.52 +- 1.717(0.283)

Mabel runs a website, and she wonders how people navigate to her website. She suspects that \[50\%\] of visitors arrive from a web search, \[25\%\] arrive from links on social media, and \[25\%\] arrive directly by entering the website's address. She plans to take a random sample of visitors and record how they navigated to the site in order to perform a \[\chi^2\] goodness-of-fit test on the results.

Shawna works for a company that makes frozen pizzas. She cooked a sample of pizzas in different ovens and let them cool in different rooms. She noticed an exponential relationship between cooling times and pizza temperatures after cooking.

204

Felipe works for a company that makes frozen pizzas. He cooked a sample of pizzas in different ovens and let them cool in different rooms. He noticed an exponential relationship between cooling times and pizza temperatures after cooking.

212

Ariana works for a company that makes frozen pizzas. She cooked a sample of pizzas in different ovens and let them cool in different rooms. She noticed an exponential relationship between cooling times and pizza temperatures after cooking.

216

The distribution of reading scale scores in the \[4^\text{th}\] grade at Truman Elementary School was approximately normal with mean \[\mu = 221\] and standard deviation \[\sigma = 36\]. Educational researchers are conducting an intervention experiment. To participate in the experiment, a student must have a reading scale score in the lower \[50\%\] of the scores in their grade level.

221

Janine is studying the relationship between the size of a diamond (in carats) and its price. She obtains size and price data for a random sample of \[64\] diamonds. Here is computer output from a least-squares regression analysis on her sample: Assume that all conditions for inference have been met. Which of these is a \[95\%\] confidence interval for the slope of the least squares regression line?

2722.34 +- 2.00(259.92)

Mrs. Fitzgerald rents a stall in a mall where she sells antiques. She earns a mean revenue of \[\$500\] per month with a standard deviation of \[\$125\]. Her stall and new inventory costs her \[\$225\] per month and are her only costs. She calculates her profits using this formula: \[\text{profit}=\text{[revenue]}-\text{[costs]}\] What will be the mean and standard deviation of the distribution of Mrs. Fitzgerald's profits?

275 125

A biologist studying largemouth bass observed a quadratic relationship between the lengths and weights of fish in a large sample. The biologist took the base \[10\] logarithm for the values of both variables, and they noticed a linear relationship in the transformed data.

3.5

A biologist studying Florida bass observed a quadratic relationship between the lengths and weights of fish in a large sample. The biologist took the base \[10\] logarithm for the values of both variables, and they noticed a linear relationship in the transformed data.

4.1

Miriam wants to test if her \[10\]-sided die is fair. In other words, she wants to test if some sides get rolled more often than others. She plans on recording how often each side appears in a series of rolls and carrying out a \[\chi^2\] goodness-of-fit test on the results. What is the smallest sample size Miriam can take to pass the large counts condition?

Maria runs a channel where she uploads and shares videos that she makes. She noticed an exponential relationship between how long her videos have been posted and the number of times each video has been viewed.

518

Mabel made a change to the website she runs, and she wonders how it affected the way people navigate to the website—from a web search, from social media, or directly by entering the website's address. She took a random sample of \[170\] visits before she made the change, and then she took a random sample of \[170\] visits after she made the change. Here are the results

Maddox read a report claiming that in his country, \[33\%\] of people's blood is O\[+\], \[30\%\] is A\[+\], \[30\%\] is B\[+\], \[4\%\] is AB\[+\], and \[3\%\] is any rh\[-\] type. He wondered if the blood types of people who donated to his blood center followed this distribution, so he took a random sample of \[200\] people and recorded their blood types. Here are his results:

Pauline sits near the snacks in the office. There are \[5\] flavors of chocolate, and she wonders if some flavors get chosen more than others. She plans to record how often each flavor gets chosen in a sample of selections to carry out a \[\chi^2\] goodness-of-fit test on the resulting data. Which of these are conditions for carrying out this test?

B + D

Maura's teacher gives multiple choice tests where each question has \[4\] choices: A, B, C, and D. Maura wonders if some of these choices appear as correct answers more often than others. She plans on taking a sample of her teacher's test questions and tallying how many times each option appears as a correct answer. She wants to carry out a \[\chi^2\] goodness-of-fit test on the resulting data.

C and D

Cason read an article claiming that \[98.6\%\] of births in his country happen in a hospital, \[0.5\%\] in a home, \[0.4\%\] in a birthing center, and \[0.5\%\] in other places. He wondered if the locations of births at his state followed this distribution, so he took a random sample of \[2000\] births and recorded where they happened. Here are his results:

Terrell's company sells candy in packs that are supposed to contain \[50\%\] red candies, \[25\%\] orange, and \[25\%\] yellow. He randomly selected a pack containing \[16\] candies and counted how many of each color were in the pack. Here are his results:

D + E

Dominik obtained a random sample of data on how long it took each of \[24\] students to complete a timed reaction game and a timed memory game. He noticed a positive linear relationship between the times on each task. Here is computer output on the sample data:

Fail to reject \[\text{H}_0\]. Dominik can't conclude a linear relationship between the times on each task.

Leona took a random sample of mobile phones and found a positive linear relationship between their battery lives (in hours) and their prices. Here is computer output from a least-squares regression analysis on her sample:

Fail to reject \[\text{H}_0\]. Leona can't conclude a positive linear relationship between battery life and price.

A group of scientists wants to investigate if they can predict the life expectancy of mammal species given its average heart rate. The table below shows the relationship between average heart rate (in beats per minute) and life expectancy (in years) for a sample of mammals.

Graph B

Every day, a store tracks how many customers make a purchase before one of them uses a coupon. The table below is a probability distribution where \[X\] represents the number of customers that make a purchase before one uses a coupon on a given day. Which graph correctly displays this probability distribution?

Graph B

An advertising company is curious about the impact the lengths of their television advertisements have on viewers' feelings about a product. They showed advertisements of different lengths to a group of volunteers and asked the volunteers to rate how positive they felt about the product on a scale of \[1\] to \[10\]. Their data is shown in the table below.

Graph C

Anuja looked up how many goals her favorite soccer team has scored in each match over the past few seasons. The table below is a probability distribution Anuja created where \[X\] represents the number of goals the team scored in a given match. Which graph correctly displays this probability distribution?

Graph C

Every week at school, a student gets chosen at random to have lunch with the principal. Here is a summary of the class year for students at the school: Which graph correctly displays the probability distribution for the class year of a student chosen in a given week?

Graph C

Lizbeth took a random sample of professional soccer players and found a positive linear relationship between how much they ran (in meters per minute) and how much they scored per game. Here is computer output from a least-squares regression analysis on her sample:

No, since \[0.660>0.05\]

Hashem obtained a random sample of students and noticed a positive linear relationship between their ages and their backpack weights. A \[95\%\] confidence interval for the slope of the regression line was \[0.39 \pm 0.23\].

Reject \[\text{H}_0\]. This suggests a linear relationship between age and backpack weight.

Reject \[\text{H}_0\]. This suggests a linear relationship between age and water consumption.

Kadence took a random sample of students at her school and asked them how much they typically slept on a school night versus a weekend night. She noticed a positive linear relationship between the times. Here is computer output from a least-squares regression analysis on her sample:

Reject \[\text{H}_0\]. This suggests a linear relationship between the sleep amounts on each type of night.

A furniture factory makes a \[4\]-piece desk. Quality control at the factory has randomly sampled numerous desk sets and determined the number of damaged pieces in each set. The table below is a partially completed probability distribution for the random variable \[X\], where \[X\] represents the number of damaged pieces in a randomly selected desk set from this factory.

[P\left(X=4\right)=0.01\]

The grades on a geometry midterm at Oak are roughly symmetric with \[\mu = 74\] and \[\sigma = 4.0\]. Nadia scored \[70\] on the exam.

\[-1.00\]

The grades on a language midterm at Loyola are roughly symmetric with \[\mu = 69\] and \[\sigma = 4.0\]. Vanessa scored \[65\] on the exam

\[-1.00\]

The grades on a history midterm at Gardner Bullis are roughly symmetric with \[\mu = 69\] and \[\sigma = 3.5\]. Ishaan scored \[65\] on the exam.

\[-1.14\]

The grades on a history midterm at Santa Rita are roughly symmetric with \[\mu = 76\] and \[\sigma = 3.0\]. Ben scored \[71\] on the exam.

\[-1.67\]

The grades on a math midterm at Gardner Bullis are roughly symmetric with \[\mu = 76\] and \[\sigma = 4.5\]. Daniel scored \[64\] on the exam.

\[-2.67\]

The grades on a math midterm at Springer are roughly symmetric with \[\mu = 78\] and \[\sigma = 5.0\]. Omar scored \[64\] on the exam.

\[-2.80\]

The grades on a math midterm at Springer are roughly symmetric with \[\mu = 68\] and \[\sigma = 4.5\]. Brandon scored \[71\] on the exam.

\[0.67\]

The grades on a physics midterm at Covington are roughly symmetric with \[\mu = 72\] and \[\sigma = 2.0\]. Stephanie scored \[74\] on the exam

\[1.00\]

The grades on a history midterm at Almond are roughly symmetric with \[\mu = 81\] and \[\sigma = 2.5\]. Luis scored \[84\] on the exam.

\[1.20\]

The grades on a language midterm at Oak are roughly symmetric with \[\mu = 67\] and \[\sigma = 2.5\]. Ishaan scored \[70\] on the exam.

\[1.20\]

Preston teaches at an international school. After reading an article about the distribution of the world's population by continent, he wanted to test if the distribution of students in his school was similar. He collected information about all \[320\] students in his school. Here are the results:

\[1.6\]

Nora, a psychologist, developed a personality test that groups people into one of four personality profiles—\[\text A\], \[\text B\], \[\text C\], and \[\text D\]. Her study suggests a certain expected distribution of people among the four profiles. Nora then gives the test to a sample of \[300\] people. Here are the results:

\[120\]

The distribution of durations for which apartments remain empty after the resident moves out for one property management company over the past \[10\] years was approximately normal with mean \[\mu = 85\] days and standard deviation \[\sigma = 29\] days. The property management company intends to update the kitchen appliances in the apartments that were empty for top \[10\%\] of durations.

\[123\]

A media streaming website knows that \[70\%\] of its customers primarily watch on their television, \[18\%\] primarily watch on their computer, and \[12\%\] primarily watch on a mobile device. The company wonders if these percentages hold true after a recent update to the product. They take a random sample of \[700\] customers and obtain these results:

\[126\]

The distribution of SAT scores of all college-bound seniors taking the SAT in 2014 was approximately normal with mean \[ \mu = 1497 \] and standard deviation \[ \sigma = 322 \]. A certain test-retake preparation course is designed for students whose SAT scores are in the lower \[25\%\] of those who take the test in a given year.

\[1279\].

Maud and Billy wanted to know if there's a difference between the modes of transportation used by men and women. One morning, they stood at the entrance to a big office building and surveyed people about the mode of transportation they used to get to the office. Maud surveyed a random sample of \[110\] women and Billy surveyed a random sample of \[110\] men. Here are the results:

\[14\]

The distribution of average wait times in drive-through restaurant lines in one town was approximately normal with mean \[\mu = 185\] seconds and standard deviation \[\sigma = 11\] seconds. Amelia only likes to use the drive-through for restaurants where the average wait time is in the bottom \[10\%\] for that town.

\[170\] second

The distribution of SAT scores of all college-bound seniors taking the SAT in 2014 was approximately normal with mean \[ \mu = 1497 \] and standard deviation \[ \sigma = 322 \]. A certain summer program only admits students whose SAT scores are in the top \[15\] percent of those who take the test in a given year.

\[1831\]

The distribution of average wait times in drive-through restaurant lines in one town was approximately normal with mean \[\mu = 185\] seconds and standard deviation \[\sigma = 11\] seconds. A journalist wrote an article about the restaurants whose average drive-through wait times were in the top \[25\%\] for that town.

\[193\]

Scientists developed a maze for rats that has \[5\] compartments, and each compartment had a different food. In each trial, scientists would record which compartment the rat went to first. They were curious if the rats favored some compartments more than others. Here are the results from \[1000\] trials.

\[200\]

The distribution of reading scale scores in the \[4^\text{th}\] grade at Roosevelt Elementary School was approximately normal with mean \[\mu = 221\] and standard deviation \[\sigma = 36\]. Students must score in the top \[20\%\] to be eligible for participation in the gifted program.

\[252\]

The grades on a math midterm at Springer are roughly symmetric with \[\mu = 72\] and \[\sigma = 4.5\]. Stephanie scored \[86\] on the exam.

\[3.11\]

Judson collected information about the name length and the population of a random sample of \[296\] American cities. Here are the results:

\[33.45\]

Lila, a marine biologist, calculated the mean \[\bar x\] and standard deviation \[s_x\] for the weights of shrimp in a sample of \[1200\] shrimp. She wanted to test how well the weights fit the 68-95-99.7 rule for normal distributions. Here are the results:

\[408\]

Jacqueline works as a quality control expert at a factory that packages different chocolates in variety packs. She selected a random container to see how well the \[220\] chocolates inside matched the advertised distribution. The table below shows the advertised distribution and the observed counts for each type of chocolate in the container she selected.

\[44\]

The dot plot shows the number of hours of daily driving time for \[14\] school bus drivers. Each dot represents a driver.

\[57^{\text{th}}\] percentile

A bakery sells cakes, cookies, and pastries. They wonder if customers are equally likely to buy each product. They take a sample of \[200\] recent purchases and record what was purchased (they are willing to treat this as a random sample). Here are the results:

\[66.67\]

Liv collected information about the length and width of a random sample of \[48\] petals of iris flowers. Here are the results:

\[7.67\]

The distribution of resting pulse rates of all students at Adams High School was approximately normal with mean \[\mu = 80\] beats per minute and standard deviation \[\sigma = 9\] beats per minute. Only students whose resting pulse rates are in the lower \[40\%\] are eligible to join the weight-lifting club.

\[77\]

The lifespans of lions in a particular zoo are normally distributed. The average lion lives \[10\] years; the standard deviation is \[1.4\] years. Use the empirical rule \[(68-95-99.7\%)\] to estimate the probability of a lion living between \[7.2\] and \[11.4\] years.

\[81.5\%\]

The lifespans of lizards in a particular zoo are normally distributed. The average lizard lives \[3.1\] years; the standard deviation is \[0.6\] years. Use the empirical rule \[(68-95-99.7\%)\] to estimate the probability of a lizard living between \[2.5\] and \[4.3\] years.

\[81.5\%\]

The lifespans of seals in a particular zoo are normally distributed. The average seal lives \[13.8\] years; the standard deviation is \[3.2\] years. Use the empirical rule \[(68-95-99.7\%)\] to estimate the probability of a seal living between \[7.4\] and \[17\] years.

\[81.5\%\]

The lifespans of gorillas in a particular zoo are normally distributed. The average gorilla lives \[16\] years; the standard deviation is \[1.7\] years. Use the empirical rule \[(68 - 95 - 99.7\%)\] to estimate the probability of a gorilla living longer than \[14.3\] years.

\[84\%\]

The lifespans of lizards in a particular zoo are normally distributed. The average lizard lives \[3.1\] years; the standard deviation is \[0.6\] years. Use the empirical rule \[(68 - 95 - 99.7\%)\] to estimate the probability of a lizard living longer than \[2.5\] years.

\[84\%\]

Ciara, an ornithologist, has \[4\] bird feeders at separate locations. She wonders if birds are equally likely to visit each of the feeders. She recorded data for a sample of \[350\] recent visits. Here are the results: Feeder\[\#1\]\[\#2\]\[\#3\]\[\#4\]Observed visits\[80\]\[90\]\[92\]\[88\]

\[87.5\]

The distribution of waist circumferences of US adult men randomly selected for a research study was approximately normal with mean \[\mu = 94\] centimeters and standard deviation \[\sigma = 11\] centimeters. A clothing store that specializes in serving larger men aims to sell clothing that will fit men with the top \[35\%\] of waist circumferences.

\[99\]

The first digits of data entries in most real-world data sets are not uniformly distributed. The most common first digit is \[1\], followed by \[2\], and so on, with \[9\] being the least common first digit. This phenomenon is known as Benford's Law. The table below is the probability distribution for Benford's Law where the random variable \[D\] represents the first digit in a data entry.

\[P(D \geq 2)=0.699\]

\[P(D \leq 2)=0.477\]

\[P(X > 2)=0.64\]

\[P(\text{at most }3 \text{ packs})=0.488\]

\[P(\text{fewer than }3 \text{ packs})=0.36\]

\[P(\text{first digit greater than }7)=0.097\]

\[P(\text{first digit less than }4)=0.602\]

Cora is playing a game that involves flipping three coins at once. Let the random variable \[H\] be the number of coins that land showing "heads". Here is the probability distribution for \[H\]:

\[P(\text{no more than }1 \text{ head})=0.5\]

LeBron James is a very popular professional basketball player in the US. Each game, players can commit a maximum of \[6\] personal fouls. Let's define the random variable \[F\] as the number of personal fouls LeBron James committed in a randomly chosen game from the 2016-2017 season. Here's the partially completed probability distribution of \[F\].

\[P\left(F=6\right)=0.03\]

\[P\left(X=4\right)=0.01\]

Blackjack is a popular card game where cards are assigned various point values. "Face-cards" and tens are the only cards worth 10 points. Each round begins with a player being dealt two cards. The table below is a partially completed probability distribution for the random variable \[Y\], where \[Y\] is the number of 10-point cards a player gets at the beginning of a round. \[P\left(Y=1\right)=\]

\[P\left(Y=1\right)=0.435\]

The distribution of annual profit at a chain of stores was approximately normal with mean \[\mu = \$66{,}000\] and standard deviation \[\sigma = \$22{,}000\]. The stores with profits in the top \[5\%\] each had a reward party for the employees to celebrate

\[\$102{,}000\]

A set of statistics exam scores are normally distributed with a mean of \[76.55\] points and a standard deviation of \[5\] points. What proportion of exam scores are between \[79\] and \[86.05\] points?You may round your answer to four decimal places.

\[\greenD{0.2834}\]

A set of art exam scores are normally distributed with a mean of \[81\] points and a standard deviation of \[10\] points. Kamil got a score of \[78\] points on the exam. What proportion of exam scores are lower than Kamil's score?You may round your answer to four decimal places.

\[\greenD{0.3821}\]

A set of average city temperatures in July are normally distributed with a mean of \[23.5 ^\circ \text{C}\] and a standard deviation of \[2 ^\circ \text{C}\]. The average temperature of Rabat is \[23 ^\circ \text{C}\]. What proportion of average city temperatures are higher than that of Rabat?You may round your answer to four decimal places.

\[\greenD{0.5987}\]

A set of sweater prices are normally distributed with a mean of \[58\] dollars and a standard deviation of \[5\] dollars. What proportion of sweater prices are between \[48.50\] dollars and \[60\] dollars?You may round your answer to four decimal places.

\[\greenD{0.6267}\]

A set of middle school student heights are normally distributed with a mean of \[150\] centimeters and a standard deviation of \[20\] centimeters. Darnell is a middle school student with a height of \[161.4\] centimeters. What proportion of student heights are lower than Darnell's height?You may round your answer to four decimal places.

\[\greenD{0.7157}\]

A set of computer science exam scores are normally distributed with a mean of \[71.33\] points and a standard deviation of \[3\] points. What proportion of exam scores are between \[68\] and \[77.99\] points?You may round your answer to four decimal places.

\[\greenD{0.8533}\]

A set of elementary school student heights are normally distributed with a mean of \[105\] centimeters and a standard deviation of \[7\] centimeters. What proportion of student heights are between \[94.5\] centimeters and \[115.5\] centimeters?You may round your answer to four decimal places.

\[\greenD{0.8664}\]

A set of average city temperatures in May are normally distributed with a mean of \[20.66 ^\circ \text{C}\] and a standard deviation of \[2 ^\circ \text{C}\]. The average temperature of Singapore is \[26 ^\circ \text{C}\]. What proportion of average city temperatures are lower than that of Singapore?You may round your answer to four decimal places. Show Calculator

\[\greenD{0.9962}\]

The lifespans of meerkats in a particular zoo are normally distributed. The average meerkat lives \[10.4\] years; the standard deviation is \[1.9\] years. Use the empirical rule \[(68 - 95 - 99.7\%)\] to estimate the probability of a meerkat living longer than \[16.1\] years.

\[\green{0.15\%}\]

The lifespans of zebras in a particular zoo are normally distributed. The average zebra lives \[20.5\] years; the standard deviation is \[3.9\] years. Use the empirical rule \[(68 - 95 - 99.7\%)\] to estimate the probability of a zebra living longer than \[32.2\] years.

\[\green{0.15\%}\].

The lifespans of gorillas in a particular zoo are normally distributed. The average gorilla lives \[20.8\] years; the standard deviation is \[3.1\] years. Use the empirical rule \[(68 - 95 - 99.7\%)\] to estimate the probability of a gorilla living longer than \[23.9\] years.

\[\green{16\%}\]

The lifespans of lions in a particular zoo are normally distributed. The average lion lives \[12.5\] years; the standard deviation is \[2.4\] years. Use the empirical rule \[(68-95-99.7\%)\] to estimate the probability of a lion living less than \[10.1\] years.

\[\green{16\%}\]

The lifespans of meerkats in a particular zoo are normally distributed. The average meerkat lives \[13.1\] years; the standard deviation is \[1.5\] years. Use the empirical rule \[(68 - 95 - 99.7\%)\] to estimate the probability of a meerkat living longer than \[14.6\] years.

\[\green{16\%}\].

The lifespans of lions in a particular zoo are normally distributed. The average lion lives \[10\] years; the standard deviation is \[1.4\] years. Use the empirical rule \[(68-95-99.7\%)\] to estimate the probability of a lion living less than \[7.2\] years.

\[\green{2.5\%}\]

The lifespans of zebras in a particular zoo are normally distributed. The average zebra lives \[20.5\] years; the standard deviation is \[3.9\] years. Use the empirical rule \[(68-95-99.7\%)\] to estimate the probability of a zebra living between \[16.6\] and \[24.4\] years.

\[\green{68\%}\]

The choir sells tickets to its performances for an assortment of prices and gives some tickets away. The choir director wants to look at the relationship between the number of seats occupied at each performance and the ticket revenue for that performance. The data show a linear pattern with the summary statistics shown below:

\[\hat y=-40.78 +9.72 x\]

An ornithologist wants to look at the relationship between the breadth of peregrine falcon eggs and the mass of the falcon chicks that hatch from them. The data show a linear pattern with the summary statistics shown below:

\[\hat y=-44.3 +1.9 x\]

Dmitri wants to look at the relationship between room temperature and the etching rate each time he has etched a circuit board with cupric chloride. The data show a linear pattern with the summary statistics shown below:

\[\hat y=1.77 +0.23 x\]

A high school counselor wants to look at the relationship between the grade point average (GPA) and the number of absences for students in the senior class this past year. The data show a linear pattern with the summary statistics shown below:s

\[\hat y=3.71-0.16x\]

A stonemason wants to look at the relationship between the density of stones she cuts and the depth to which her abrasive water jet cuts them. The data show a linear pattern with the summary statistics shown below:

\[\hat y=374.2 -133 x\]

A fuel consortium chairman at an airport wants to look at the relationship between cost of crude oil and the cost of jet fuel. The data show a linear pattern with the summary statistics shown below:

\[\hat y=5.33 +1.13 x\]

A personal trainer wants to look at the relationship between number of hours of exercise per week and resting heart rate of her clients. The data show a linear pattern with the summary statistics shown below:

\[\hat y=86.05 -1.32 x\]

\[\red{15.85\%}\]

The lifespans of tigers in a particular zoo are normally distributed. The average tiger lives \[22.4\] years; the standard deviation is \[2.7\] years. Use the empirical rule \[(68-95-99.7\%)\] to estimate the probability of a tiger living between \[27.8\] and \[30.5\] years.

\[\red{2.35\%}\]

A biologist observed a curved relationship between the average heart rates and life expectancies of several mammal species in a large sample. The biologist took the natural logarithm for the values of both variables, and they noticed a linear relationship in the transformed data.

\[\widehat{\ln(\text{LE})}=6.33-0.78\ln(\text{HR})\] = 15 or 9 or 23

Chaya took a random sample of \[49\] girls in her high school and let them play a memory game. She also took the participants' heights (in \[\text{cm}\]). Here is computer output on the sample data:

\[t=\dfrac{-0.075}{0.056}\]

Nkechi took a random sample of \[10\] countries to study fertility rate (babies per woman) and life expectancy (in years). She noticed a negative linear relationship between those variables in the sample data. Here is regression output on the sample data:

\[t=\dfrac{-5.973}{0.587}\]

Kadence took a random sample of \[24\] students at her school and asked them how much they typically slept on a school night versus a weekend night. Here is computer output from a least-squares regression analysis on her sample:

\[t=\dfrac{0.789}{0.237}\]

Zoie took a random sample of \[26\] counties in her state and collected data regarding each county's population and waste (in tons). Here is computer output on the sample data:

\[t=\dfrac{0.853}{0.025}\]

Elvin collected the scores of a random sample \[41\] students on the first exam in a certain class and their corresponding scores on the second exam in that class. Here is computer output on the sample data:

\[t=\dfrac{0.881}{0.11}\]

Cerro Negro is an active volcano located in Nicaragua. Amina gathered data on the date and volume (in thousand cubic meters) of Cerro Negro's \[23\] recent eruptions. Here is regression output on the sample data (years are counted as number of years since 1850):

\[t=\dfrac{1198}{131}\]

Ona took a random sample of \[20\] soccer teams across Europe, and tracked the average number of goals each team scored per match, and how many total matches each team won, in the \[2014\,\text{-}\,2015\] season. Here is regression output on the sample data:

\[t=\dfrac{14.02}{1.15}\]

Jian obtained a random sample of data on how long it took each of \[24\] students to complete a timed reaction game and a timed memory game. He noticed a positive linear relationship between the times on each task. Here is computer output on the sample data:

\[t=\dfrac{14.686}{13.329}\]

Amos collected data about population density (in thousand people per square kilometer) and average rent for \[1\]-bedroom apartments in a random sample of \[25\] cities. Here is regression output on the sample data:

\[t=\dfrac{22.615}{4.179}\]

A marine biologist wanted to construct a \[t\] interval to estimate the mean weight of marine otters using \[98\%\] confidence. They took a random sample of \[n=8\] marine otters to measure their weights. These weights were roughly symmetric with a mean of \[\bar x=4.5\,\text{kg}\] and a standard deviation of \[s_x=1.1\,\text{kg}\].

\[t^{*}=2.998\]

A market researcher for a communications company took a sample of \[300\] customers to see if those with children were more or less likely to pay for upgraded internet speeds. Here are the outcomes and partial results of a chi-square test (expected counts appear below observed counts):

In basketball, a team can score from \[3\]-point shots, \[2\]-point shots, and \[1\]-point shots. Last season, a team recorded what type of shot each attempt was. The coach wonders if the attempts from the current season reflect the distribution from last season. Here are results from a sample of \[40\] attempts from the current season along with a chi-square goodness-of-fit test:

The human resources department at a large company regularly conducts an employee satisfaction survey. One item on the survey presents employees with the statement, "I am happy overall at work." Based on historical data, here is the distribution of responses to this item:

The owners of a large shopping complex wondered how their customers traveled to the complex. They surveyed a random sample of \[100\] customers. Here are the outcomes and partial results of a chi-square test (expected counts appear below observed counts):

The principal of a large middle school wondered whether students in each grade kept their lockers equally neat. They selected random samples of \[30\] lockers belonging to students in each grade. Here are the outcomes and partial results of a chi-square test (expected counts appear below observed counts):

A city has \[4\] voting districts. Records from previous years show what proportion of residents live in each district. A political analyst wondered if those proportions still held true, so they took a random sample of \[120\] residents. Here are their results along with a chi-square goodness-of-fit test:

A forest is divided into \[4\] regions by a road and a stream. A wildlife researcher was curious if the number of deer living in each region corresponded to the total area of each region. They used drones to take overhead images and counted how many deer were in each region. The following table shows the proportion of total area for each region of the forest and how many deer were observed in each region along with a chi-square goodness-of-fit test.

An educational researcher wonders if students in their state are uniformly distributed across grades \[5\] through \[8\]. Here are results from a random sample of \[719\] students along with a chi-square goodness of fit:

Plamen is a social media manager for a large company. He takes a random sample of their posts to see if there is a relationship between the time of each post and the number of times the post gets shared. Here are the outcomes and partial results of a chi-square test (expected counts appear below observed counts):

The following table shows the approximate distribution of scores on the AP Latin exam in 2017:

A group of nutritionists wondered whether there was an association between gender and the kinds of food a person likes to eat. They surveyed a random sample of \[231\] people about their favorite foods. Here are the responses and partial results of a chi-square test (expected counts appear below observed counts):

Elsa is investigating rider complaints that a certain bus route is only on time \[60\%\] of the time, is early \[25\%\] of the time, and is late the remaining \[15\%\] of the time. She took a random sample of \[45\] times and recorded whether the bus was on time, early, or late. Here are her results:

Market researchers wonder if people in different countries have different preferred sports to watch during the winter Olympics. They take a random sample of people from each country and survey them about their favorite sport to watch. Here are the responses and partial results of a chi-square test (expected counts appear below observed counts):

Salma operates a ramen restaurant. Historically, half of customers order pork ramen, and the other half of customers are split evenly between chicken and vegetarian ramen. Salma modified the chicken and vegetarian recipes, and she wonders if customers' ordering habits will change. Here are results from a sample of \[32\] orders after launching the new recipes along with a chi-square goodness-of-fit test:

c or d

A group of researchers wondered whether there was an association between handedness and which foot was longest. They took a random sample of people, measured their feet, and recorded their handedness. Here are the outcomes and partial results of a chi-square test (expected counts appear below observed counts):

A group of researchers wondered whether vegetarians favored different seasons than non-vegetarians. The researchers took a random sample of people and surveyed them about their favorite season and whether or not they were vegetarian. Here are the responses and partial results of a chi-square test (expected counts appear below observed counts):

June is a researcher. She read a 2016 study that published the following population distribution for Americans:

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