Probability and stats Practice problems

Students are given a spinner with 5 equal sectors numbered 1-5. They are instructed to spin 50 times and record the number the arrow lands on. If there are 5 groups of students spinning, which of the following is most likely the total number of times the spinner lands in the 3 sector?

48

A grocery store in a small town plotted the number of items bought per visit versus the shopper's age. The linear regression equation of the data is y = -1.12x + 100 and r2 = 0.62. Which of the following represents the value of the coefficient of determination?

0.62

On average, a personal computer is used for 7 years before it is replaced. Computer replacement can be modeled with an exponential distribution. What is the probability that a personal computer will be used for 12 years before it is replaced?

2.6%

Approximately what fraction of the population is within one standard deviation of the mean in a dataset with a normal distribution?

2/3

Rohan rolls a 10 sided dice with sides numbered from 1 to 10. What is the probability that he rolls a prime number?

2/5

Student council members are selling valentine cards as a fundraiser. They make $0.50 for each card they sell and want to sell 750 total. The graph shows the number of cards that have been sold thus far by each grade. How many more must be sold overall to meet their goal?

200 cards

The scatterplot suggests a trend between variables x and y. Which of the following best describes the trend?

As x increases, y increases

What can be said about the graph of the data below?

It is skewed left.

Edward wants to make a plot that depicts his classmate's favorite types of juice. Which of the following plots would be best suited for that?

Pie Chart

Which statement correctly describes information about the following set of data? {8, 10, 12, 14, 14, 26}

The mean is greater than the median.

Which of the following qualifies as a binomial experiment?

The probability of rolling a 7 during 4 out of 6 rolls of a standard pair of dice.

The table above shows the total precipitation each month. What is the average amount of precipitation in a month?

11

What is the mean of the data set below? 15, 18, 19, 54, 74, 94, 67, 82, 48, 31, 15

47

Which of the following is indicated by a residual plot in which the data are randomly scattered about the x-axis?

A linear model best represents the data.

Mr. Schmidt is teaching statistics and the data lists are long. Finding the mean would take a long time so he has decided students may bring a calculator from home to use on the unit test. What can he do to ensure that all students have a device?

Give advance notice to bring calculators and provide devices for those who do not have one.

Which of the following is the best description of why statisticians report the confidence level along with survey results?

The confidence level indicates how sure the statistician is that the sample outcomes model the population outcomes.

A combination lock is opened by setting each of five barrels to the correct digit. If digits are randomly chosen from the digits 0 through 9, how many unique combinations can be generated? Repetition of numbers is allowed.

(10^5)

Mrs. Kade gave a math quiz to her students. Score Number of Students 60 3 70 4 80 9 90 8 100 5 The scores are listed in the data table. Which of the following is closest to the average score?

83

The data above is presented in a stem and leaf plot. The data represents the grades on a recent math test given by Mr. Davis and Mrs. Smith. How do the means for Mr. Davis' class and Mrs. Smith's class compare with each other?

Mr. Davis' class has a mean of about 76, 2 points lower than Mrs. Smith'

Which of the following pairs of measures of center indicates positive skew in a normal distribution?

x =m and m<Dm<D

The scatterplot shows the sales, s, for a local ice cream store based on the daily high temperature, t. There is a strong linear correlation between s and t. Based on the relationship, which of the following is the best estimate of the increase in sales for 1℃ increase in temperature?

$30

What is the median and mean of the data set below? 10, 8, 5, 3, 7, 4, 5, 9, 2, 3, 7, 3, 8, 6, 4, 1, 2, 1, 10, 3

median: 4.5; mean: 5.0

John wants to make a boxplot of a large data set. What should he do first?

Order the numbers in his data set from lowest to highest.

At the basketball game last night, all 12 players scored. The percentage of players that scored each point value is shown in the histogram. Which table accurately shows the data as a list of the total points per player?

Table A

What can be said about the graph of the data below?

It is skewed right.

The range of savings account balances for the students in Mrs. Jones class is $210. If the student with the mosts savings has $220 in savings, how much does the student with the lowest amount of savings have?

$10

Mrs. Spiser is teaching students about populations and samples in mathematics. They will take a survey to see how many students are buying lunch in the cafeteria from the sample and then they will compare it to the whole class. What is the best method to use?

As students enter her room, they randomly draw a red or black card. She teaches the concept by explaining that the class is the population and students who drew a red card are the sample group.

Five cards are randomly chosen without replacement from an ordinary deck of 26 black and 26 red cards. What expression shows the probability that all five cards are red?

( 52 26 ​ )( 51 25 ​ )( 50 24 ​ )( 49 23 ​ )( 48 22 ​ )

A class of students is learning about sampling methods and are told to ask people whether they prefer going for a walk or napping. Students bring back the results after sampling parents, siblings, and friends. Which type of sampling method best describes how the students obtained their results?

convenience sampling

A student tosses a six-sided die, with each side numbered 1 through 6, and flips a coin. What is the probability that the die will land on the face numbered 1 and the coin will land showing tails?

1/12

Six cards were randomly pulled from a deck of cards. The values of five of the cards were 4, 6, 9, 3, and 1. The mean of the six cards is 5. What is the value of the sixth card?

7

The dot plot shows 48 values. Which of the following statements is true?

The range is greater than the median.

Mrs. Rogers gave a test to her 6th-grade math class. The scores on the test were as follows: 65 72 79 84 84 86 87 88 89 91 92 If the mean is determined to the nearest whole number, by how much do the mean and median differ?

3

What is the range and mode of the data set below? 10, 8, 5, 3, 7, 4, 5, 9, 2, 3, 7, 3, 8, 6, 4, 1, 2, 1, 10, 3

range: 9; mode: 3

A bin of balls in gym has 60 total balls. 15 are soccer balls and the rest are a mixture of volleyballs and basketballs. If one ball is taken at random, the probability of drawing a basketball is 4/15. How many of the balls are volleyballs?

29

Brianna spun each of the two spinners. What is the probability that she did NOT spin a "1" on the second spinner?

3/4

How many different outcomes are possible when a pair of standard six-sided dice are rolled?

36

The data shown is presented in a stem and leaf plot. The data represents the grades on a recent math test given by Mr. Davis and Mrs. Smith. What is the median score for Mr. Davis' class?

80

Which stem and leaf plot matches the data in the histogram shown? Histogram

Graph D

Which of the following is true for a small standard deviation?

The data are closely grouped around the mean.

Students are learning about probability. The teacher explains the theoretical probability of a two-sided coin landing on any one side. Students then work in groups and flip a two-sided coin several times. The first group of students flips the coin 20 times and finds the coin lands on side A 13 times and side B 7 times. Which of the following observations, based on the scenario, about probability is accurate?

The theoretical probability of the coin landing on side A is less than the experimental results recorded.

Which of the following dispersion values equal the range and the interquartile range for the set of class scores shown below? 52 58 65 72 73 73 74 78 81 86 90 94

range: 42 interquartile range: 18

A teacher tells the students the mode of the scores on the most recent exam was 85. Which of the following is the most accurate interpretation of the result?

The most common score on the test is 85 percent.

The debate team has averaged 108 points in the last 5 tournaments. If they scored 120, 98, 92, and 108 in the first 4 tournaments, how many points were scored in the fifth tournament?

122

According to the graph shown, which of the following best approximates the maximum difference between the amount of energy consumed from fossil fuels and that consumed from renewable sources in any one year?

78 quadrillion btu

A teacher carries around a bag of marbles with 10 of each of the following colors: blue, white, and yellow. She asks students to draw one marble from the bag. Before they draw, they must state the probability of drawing a certain color. The first student says the probability of drawing a blue is 1 out of 3 because 10 out of 30 simplifies to 1:3. The student holds onto his blue marble and the next student says his probability of drawing yellow is 1:3. Evaluate his statement.

It is incorrect and a common misconception about dependent events.

A survey was taken to determine the number of students in a sample were voting for Maria in the next student council election. The results indicated that 63% of the student body would vote for Maria with a margin of error of 5%. Which of the following statements is true?

Maria is likely to win more than 50% of the vote.

Which of the following statements can be inferred from the graph? Select all answers that apply.

The city with the most rainfall over three years had more than 160 inches of precipitation. The total approximate precipitation for 2010 was 210 inches. The next closest year was 2011 at 175 inches. The precipitation in Springfield more than tripled from 2009 to 2010.

The test scores in Mrs. Marsala's math class are as follows: 72 75 78 84 88 89 91 92 93 94 97 What is the range of scores?

25

Which of the following is true of a statistical experiment?

Its outcome is determined by chance.

Jessie draws a marble from the bag shown and then, without replacing the first marble, he draws a second one. Which expression shows the probability that he drew a red marble both times?

3/10 • 2/9

The scatterplot suggests a trend between variables x and y. Which of the following best describes the trend?

As x increases, y decreases

Which equation most closely represents the line of best fit for the scatterplot shown?

y= 2 3 ​ x+1

The probability that event NN will occur is 0.74. The probability that event NN and event OO will occur is 0.1628. If NN and OO are independent events, what is the probability that event OO will not occur?

0.78

John creates a probability model for rolling two six-sided die as shown above. The value of each die is on the outside, the sum of the two is on the inside. What is the probability of rolling two dice and having a sum of 4?

1/12

Rae Anne has 3 children. The first is a boy, the second is a boy, and the third is a boy. What is the probability that her fourth child is also a boy?

1/2

Mrs. Harris writes all the numbers from 4 to 24 on slips of paper and places them in a hat. She then asks a student to pick a number from the hat. What is the probability that the number chosen by the student will be a prime number?

1/3

The circle graph shows the results of a survey of 150 students. How many students chose basketball as their favorite sport?

12

What is the median of the data set below? 15, 18, 19, 54, 74, 94, 67, 82, 48, 31, 15

48

Of the 40 prizes in the toy box, 15 are slime, 18 are fidget spinners, and 7 are candy. If a student reaches in the box and randomly draws a prize, what are the odds it is not slime?

5/8

What is the mode of the data set? 22 23 30 38 45 46 48 55 55 60 61 63 67 70 77 80 93 95 97 99 100

55

A gumball machine is filled with 23 blue gumballs, 26 red gumballs, 18 yellow gumballs, and 22 green gumballs. When a penny is inserted into the machine, a gumball is released. José inserts a penny into the machine and receives a green gumball. What is the probability that the next person to insert a penny will NOT receive a green gumball?

67/88

Michelle is assigned homework to flip a coin 10 times, then 100 times, then 1000 times. She decides to use a use her computer to generate a 1 for heads or a 2 for tails. She has the following results: Number Of Trials Number of Heads (1s) Number of Tails (2s) 10 7 3 100 45 55 1000 507 493 What can be said about the results of her simulation?

As she performed more trials, the experimental probability became closer to the theoretical probability.

A grocery store in a small town plotted the number of visits per month versus the distance between a shopper's home and the store, as shown. Which of the following describes an inference that can be made from the data shown in the graph? Select all answers that apply.

Overall, shoppers who lived near the store visited the store more often than shoppers who lived further away. There is a negative correlation between the number of visits to the store and the distance between home and store.

Students examine the results of 4 sample surveys. Which of the following surveys is likely to have the largest level of confidence?

Sample size = 400; outcome = 75% pro and 25% con

The following is a list of test scores from the most recent Biology test in Ms. White's class. Which of the following is most clearly evident in the set of data? 52 58 65 72 73 73 74 78 81 86 90 94

a cluster

A grocery store in a small town plotted the number of visits per month versus the distance between a shopper's home and the store, as shown. The linear regression equation of the data is y = -1.12x + 100 and r2 = 0.62. Which of the following best describes the correlation between the data?

a rather strong negative correlation

The graph shows the number of students in a high school over a 50-year period. Between which years did the number of students increase by the greatest amount?

between 1980 and 1990

Mrs. Smith wants to analyze the test scores of her 6 classes. What is the most appropriate way to represent her test score data so she can compare her different classes?

box and whisker plot

Mr. Lemon is introducing a new concept: bivariate data analysis. He knows that most students would not recognize the word, "bivariate" so he asks students to break the word into parts and identify what the prefix "bi-" means. Which goal is he most likely trying to achieve?

building on prior knowledge

Which of the following best describes data with a geometric distribution?

data with a finite number of outcomes that produce the number of trials needed to obtain the first success

Fat has 9 calories per gram whereas carbohydrates and proteins each have 4 calories per gram. What is the weighted average, in calories per gram, of a meal with 34 grams of fat, 41 grams of protein, and 81 grams of carbohydrates?

5.1 Cal/g

Chelsea made a quick trip to the store to pick up 6 items. The costs of the items are listed below. What is the range of the prices for this trip? $2.31, $1.97, $2.58, $2.87, $1.54, $2.86

$1.33

What percent of the total energy from all sources comes from natural gas?

29%

The local radio station is giving away free concert tickets to the 104th person who calls in. Andrew and John want to win the concert tickets, so Andrew calls into the station 6 times and John calls in xx times. If the probability that either Andrew or John wins the concert tickets is 0.125, what is the value of xx?

7

The scores of the top quartile of students in a math class were 95, 86, 87, 91, 94, and 87 on the last test. What is the average score of the top six students?

90

Carrie conducts a random survey of 125 seniors at her high school about their lunch habits. Of the 125 students she surveyed, 50 students reported that they eat fast-food for at least 2 lunches a week. Which of the following statements is a reasonable conclusion for her statistical study?

Carrie concludes with 95% confidence that the true proportion of seniors at her school who eat at least two fast-food lunches a week is between 31% and 49%.

The students in Mr. Zou's class are having difficulty selecting the correct distribution model for various experiments. Which of the following is the most likely to help students learn to differentiate between the models?

Have students work in small groups to categorize several experimental descriptions, then lead a class discussion on the reasons for their categorizations.

In the pair of dice that Tim rolled 25 times, he recorded a sum of 4 on three of those rolls. What is the difference between the theoretical probability and the experimental probability of rolling a pair of dice and getting a sum of 4 based on Tim's experiment?

The experimental probability is about 4% greater than the theoretical probability.

Señora Gomez teaches Spanish at Bill Cline Preparatory School. The number of students in each of her classes is shown in the bar chart.

The median is 28.

The scatterplot shows the relationship between ice cream sales and the temperature outside. How can this relationship best be described?

There is a positive linear correlation between temperature and sales.

The list shows eleven scores from a recent math quiz. The range of the eleven scores is 10, and the interquartile range is 7. Which of the following could be the value of x? 21, 25, 19, 18, 19, 15, 25, 16, 23, 16, x

f x = 17,

Students in Mr. Miller's class are given a worksheet with the different combinations that can be reached when flipping a coin and rolling a standard die. Students then work in pairs to flip and roll all of the combinations. What topic is Mr. Miller teaching

sample space

Scores on a pre-unit test were compared to scores on a post-unit test and graphed on the scatterplot. What type of correlation is seen on the graph?

weak positive

The partially completed graph shows the attendance for the Houston Rodeo, excluding Saturday. If 156,000 people attended throughout the week, where should the bar for Saturday end?

35

Calculate the mean weight of a group of apples with the following individual weights: 4.6, 4.9, 5.5, 5.8, 6.0, 6.4, 6.5, and 5.8 ounces

5.7

A randomized poll was conducted at the high school. Of the 2500 students that were surveyed, 28 out of every 35 spend more than an hour each day on homework. Estimate the number of students who spend less than an hour each day on homework.

500

Answer the question based on the circle graph below. If there are 300 students in the grade, how many more students prefer chocolate ice cream to vanilla?

54

The data shown is presented in a stem and leaf plot. The data represents the grades on a recent math test given by Mr. Davis and Mrs. Smith. What is the range for Mrs. Smith's class

57

The data table shown describes how students get to school each morning at Memorial Middle School. If a student is drawn at random from the walkers and bus riders, what is the probability they are a walker?

7/44

A teacher's goal in a math lesson to have students extract data from various charts and displays. What is the best way to do this?

Give each student a chart or display and have them create questions and then trade with a partner.

Mrs. McCauley is asking students about statistical experiments. Most students are giving brief answers and justifications. What can she do to increase student participation?

Give sentence stems and time to think before calling on someone.

Mrs. Gore is teaching about simple and compound events in probability. As she walks around the room, she has students draw a marble from a bag and answer the probability of drawing certain colors. What is the main motivation for teaching it this way?

Giving students an interactive way to learn

A mathematics teacher determines that the median score for the most recent test was 80 percent. Which of the following is the most accurate interpretation of the result?

Half the students scored below 80 percent.

Sally and Susie place 30 white marbles and 9 black marbles in a sack. They play a game where the object of the game is to accumulate more white marbles than the other person. On each turn a person can take as many marbles as they would like, but if they grab a black marble then they must return all their marbles taken on that turn. On Sally's turn she picks up 3 white marbles and no black marbles. If Susie grabs one more marble, what are the odds that she will grab a black marble? (Note: Sally does not return her 3 marbles to the sack.)

1 in 4

10 groups of 5 students spin the spinner shown. If each student spins the spinner 6 times, what is the expected number of times the spinner would land on A for all 10 groups of students? There is an equal chance the spinner lands on A, B, or C.

100

Tim rolls a pair of dice 25 times and records the sum of the numbers shown. How many different sums are possible?

11

A 6-sided die is rolled 100 times with the results shown in the table. Outcome 1 2 3 4 5 6 Frequency 20 18 22 20 16 4 What is the experimental probability of rolling a 3?

11/50

The formula for permutations is: nPr = \frac{n!}{ \left( n-r \right) !} (n−r)! n! ​ while the formula for combinations is: nCr= \frac{n!}{r! \left( n-r \right) !} r!(n−r)! n! ​ . How many 3-letter combinations can be formed from the word "mathematics" where MAT is the same as ATM?

165

During one year, a certain school district reported a total enrollment of 85,679 students. The district math scores of the students were modeled with a normal distribution. The mean raw score was 56 with a standard deviation of 10.4. Based on this distribution, which of the following is the best estimate of the number of students with a raw score of 35.2 or lower on the test during that year?

2,140

Whitney is packing for a week-long trip. She fills her suitcase with 5 shirts, 3 pairs of pants, 2 skirts, and 2 dresses. If an outfit consists of 1 shirt and 1 bottom (pant or skirt) or 1 dress, how many different outfits can Whitney create?

27

John's family decided to drive to a beach that was 60 miles from their house. There was a great amount of traffic and their average speed was 30 miles per hour. Thirty minutes after they arrived at the beach, it began pouring rain. They ran back to the car and headed home. It took half as long to get home as it did to arrive at the beach. Which graph shows their distance from home in miles related to the time it took to make the trip?

Graph B

A laboratory sample initially contains 1.2 g of radioactive material. After 8 days, the sample contains 0.6 g of the material and after 16 days, the sample contains 0.3 g. Which of the following functions best models the mass M of the sample as a function of time t, in days?

M(t)=1.2( 2 1 ​ ) t/8

Mr. Thomas is teaching measures of central tendency to his class that is mostly comprised of English Language Learners (ELL). What is the best support for teaching the new vocabulary words?

Put the words on a Word Wall with the word, picture, and definition.

Which of the following sampling methods is often used to ensure representation from all genders and races?

stratified sampling

Which of the following scatterplots is most likely to have a line of best fit represented by the equation below? y=-4x+3y=−4x+3

Graph D

Mrs. York created a box plot to analyze her students' grades from their unit exam. The scores were as follows: 85, 65, 75, 90, 58, 60, 60, 80, 89, 75, 54, 100, 88, 88, 68, 59, 100, 88, 57, 77 Which of the following box plots best matches her data?

Graph D

Without looking, Jessie draws a marble from the bag shown, replaces it, gives the bag a good shake, and draws again. What is the probability that Jessie drew a red marble both times?

3/10 • 3/10

The graph shows the number of students graduating from a local community college between 1999 and 2003. According to the graph, how many students graduated before 2001?

320

A student was selected as a captain of a cooking team in a consumer and family studies class. The student could pick 2 of 5 girls and 3 of 7 boys to be on their team. What is the total number of different teams that this captain could select?

350

Third-grade students at Grace Moore Elementary just completed a math test. The number of questions missed by each student is graphed. How many students missed more than 2 questions on the test?

46 students

While at the vet's office, Susanna saw a chart of the weight ranges of golden retrievers. She determined that her own retriever was in the 70th percentile of the weights of the dogs on the chart. Which of the following is true?

About 30% of golden retrievers weigh as much as or more than Susanna's dog.

What is the probability that the sum of the two dice is between 2 and 12, inclusive?

1

What is the mode of the data set below? 1.8, 1.5, 2.4, 2.1, 1.5, 2.1, 1.7, 1.5, 1.8

1.5

Jon is in the eighth grade and takes a standardized math test. Use his test scores, shown, to answer the following question. Raw Score Percentile Stanine Grade Equivalent 64 79 6 7.8 Which of the following can be concluded from Jon's test score?

21% of the test takers scored as well as or better than Jon.

The graph shows the approximate population of the United States beginning in 1970. Assuming the population trend continued in the same manner, what would be a reasonable estimation for what the population of the United States was in 2010?

290 million people

Kate surveyed the senior class at her high school to find out if they prefer to go to the movie theater or a school sporting event on their Friday nights. Of the 75 students she randomly selected and surveyed, 24 said they prefer to go to the movies. If she has 800 seniors at her school, how many seniors could she expect to show up to the sporting event this week?

544

Ben wants to determine the effect of minutes studied on test grades. He collects data from students in his class about how much they studied and their exam grades. He creates the following scatterplot: What can he conclude about studying?

Studying has a positive correlation with exam grades.

Brianna spun each of the two spinners. Which expression depicts the probability she spins an "A" on the first spinner and a "1" on the second?

1/3 • 1/4

The geometric probability function is f \left( x \right) = \left( 1-P \right) ^{x-1}Pf(x)=(1−P) x−1 P. What is the approximate probability of rolling a standard die and getting the first 6 on the 3rd try?

12%

The formula for permutations is: nPr = \frac{n!}{ \left( n-r \right) !} (n−r)! n! ​ while the formula for combinations is: nCr= \frac{n!}{r! \left( n-r \right) !} r!(n−r)! n! ​ . As a warm-up, Ms. Caulkins asks her students to compare these two formulas and identify the differences and similarities before she has taught what the formulas are used for. What is her goal in this exercise?

activating prior knowledge of reducing fractions

Which of the following are statistical experiments? Select all answers that apply.

flipping a coin 12 times rolling two dice until you get doubles rolling a die 6 times in a row

A grocery store in a small town plotted the number of visits per month versus the distance between a shopper's home and the store, as shown. The linear regression equation of the data is y = -1.12x + 100 and r2 = 0.62. The slope of the equation can be interpreted as:

for every 1-mile increase in the distance between the shopper's home and the store, the average number of visits decreases by 1.12.

In an effort to teach outliers, Mr. Newt asked students to evaluate a sample of ages for the measures of central tendency and range. Half of the groups used data from only the students while the other half used data from the students and Mr. Newt. Then they compared their final numbers. What was his purpose in using the method?

providing a real-world example of mathematical outliers

Which of the following best describes the relationship described by bivariate data?

The relationship between two variables.

A grocery store in a small town plotted the number of items bought per visit versus the shopper's age. Which of the following describes the type of relationship shown in the graph?

bivariate