Probabilities and Statistics
A pair of 6-sided dice are rolled. What is the probability that both numbers are less than 3?
1/9
A study is being done to determine the effect of the price for an item in dollars on the profit for the item in dollars. Which numerical measure is appropriate?
Correlation coefficient
A spinner has 3 equally sized colored sections. The colors are Red, Green, and Blue. A coin has two sides: heads and tails. What is the sample space for spinning the spinner, then flipping two coins?
{RHH, RHT, RTH, RTT, GHH, GHT, GTH, GTT, BHH, BHT, BTH, BTT}
At a security patrol business, a manager notices that more security guards call off when the temperature is low. The manager obtains a correlation coefficient of r = -0.79. Using just this information, what can be concluded?
There is a negative association between temperature and security guard absences.
A shipment of two packages is being sent from Europe to the United States. One package weighs 30.5 kilograms while the other weighs 16 kilograms. How many pounds does the total shipment weigh? Round your answer to the nearest tenth.
102.3 pounds
If A and B are two events and P(A) = 0.63, P(B) = 0.7, and P(A and B) = 0.13, what is P(B|A) equal to?
21%
A pair of 6-sided dice are rolled. What is the probability that the numbers on the dice add to a number greater than 9?
0.167
There are 125 people at a restaurant and 100 of them are adults. What is the probability of randomly selecting a person that is not an adult?
0.20
The Cardinals have lost 62 of their 162 games. Using only this data, what is the probability that the Cardinals lose a game?
0.38
A financial advisor is examining the performance of their clients' holdings to better inform his decisions. The client has 70% invested in stocks and 30% invested in bonds. It was found that 72% of the stocks saw an annual gain. Additionally, it was found that 15% of the bonds saw an annual loss. What is the probability that an investment is a stock that had an annual gain?
0.504
There are 10 black, 6 blue, 12 yellow, and 4 red cars in a parking lot. What is the probability of randomly selecting a car that is not yellow?
0.635
There are black, blue, and white marbles in a bag. Two marbles are drawn from the bag without replacement. The probability of choosing a black marble first is 0.45. The probability of choosing a black marble first and then a white marble second is 0.3. To the nearest hundredth, what is the probability of the second marble being white if the first marble chosen is black?
0.67
If the probability of a sunny day is 0.6, the probability of the date on the calendar being an odd number is 0.5, and the probability of a day being sunny and having an odd number on the calendar is 0.3, what is the probability of the calendar date being odd or it being a sunny day?
0.8
A student is studying their flashcards that they made for the course. They will read the definition on one side of the card and then try to guess the correct vocabulary word. Since we don't know how long the student has been preparing for the course, assume that guessing correctly and incorrectly are equally likely. If they pick three flashcards to quiz themselves, what is the probability that they get at least two of them correct?
1/2
A coin has two sides: heads and tails. If three coins are tossed, what is the probability of all three coins landing on the same side?
1/4
A box contains one red ball, one purple ball, and one blue ball. Two balls are drawn from the box without replacement. What is the probability of selecting a red ball and then a purple ball?
1/6
A jar contains 4 red candies and 7 green candies. Two children each randomly select one piece of candy from the jar to eat. What is the probability that the second child selects a red candy if the first child has already selected a red candy?
3/10
At a work function, the boss is handing out donuts. You are the last person in line and decide to ask if you can have two donuts (instead of one). There are five strawberry frosted donuts and three chocolate donuts left. If your boss randomly picks two donuts for you, what is the probability that you get two chocolate donuts?
3/28
A coin has two sides: heads and tails. If three coins are tossed, what is the probability of getting exactly two heads?
3/8
A normally distributed data set has a mean of 50 and a standard deviation of 7. Which two values does 68% of the data fall between?
43 and 57
There are 43 dogs and 50 cats available for adoption at an event. If an animal is randomly chosen, what is the probability a dog will be selected?
43/93
A normally distributed data set has a mean of 115 and a standard deviation of 5. What percent of data falls between 100 and 115?
49.85%
The probability that Bowie walks to work is 25%, the probability that Bowie bikes to work is 30%, and the probability that Bowie drives to work is 45%. On a randomly selected day, what is the probability that Bowie walks or bikes to work?
55%
There are 32 houses with privacy fences, 45 houses with chain-link fences, and 23 with no fences. What is the probability of selecting a house that does not have a chain-link fence?
55%
Researchers for a pet food company found that 48% of homeowners have a dog, 27% have a cat, and 18% have both a dog and a cat. What is the probability that a randomly selected homeowner will have a dog or a cat?
57%
The number of hurricanes that have occurred each year in the United States over a ten-year period are given below. Find the median. 4, 4, 6, 8, 9, 9, 5, 5, 3, 16, 15
6
The weekly service calls for a specific brand of office copier are listed in the table below. Find the median. Number of Service calls / Frequency 4 / 2 5 / 1 6 / 3 8/ 5 9 / 2
8
Test scores are provided in the stem plot below. Find the mean and round to the nearest whole number. Stem / Leaf 5 / 2 6 / 7 / 1, 3, 3, 5, 9 8 / 5, 5, 5, 8 9/ 3, 5, 8
81
A teacher was collecting data comparing student absences and final grades. They performed a least squares regression analysis on the data and finds the least squares equation to be y = -3.6x+100, where x is the number of student absences and y is the predicted final grade, in percentage. Using the given least squares equation, what is the estimated final grade for a student who was absent 4 times?
85.6
A town wants to know what its business owners think of a plan to install new lighting downtown. Which sampling frame should they use?
All business owners in the town.
A dot plot would be an appropriate display for which of the following types of website data?
Average number of button presses by visitor
A company has 10 employees. There are four salespeople, three accountants, one quality assurance employee, and two human resource employees. Which type of graph should be used to display how many employees work in each position?
Bar graph
_____ are used to display quantitative data, but they ignore individual data values.
Box Plots
A study was done to see if pet ownership influenced test scores. Which type of classification is this?
Categorical to quantitative
A study analyzed the on-time performance (on-time vs. late) of Contractor A versus Contractor B for building repairs. Which numerical measure is appropriate for this study?
Conditional percentages
A social media content producer is looking at how many views their videos got when they did videos by themselves versus when they collaborate with other content producers. What numerical measure is appropriate for this situation?
Five-number summary
There are red, yellow, and brown cereal boxes to choose from. The probability of choosing a red box is 0.28, the probability of choosing a yellow box is 0.35, and the probability of choosing a brown box is 0.37. If the probability of choosing a brown box given that a red box is already chosen is 0.75, what is the correct notation that explains this?
P(brown|red) = 0.75
Customers purchasing a product were surveyed on their education history and given the following choices: High School Diploma/GED, Associate's Degree, Bachelor's Degree, Master's Degree, Professional Degree/PhD. Which graphical display should be used?
Pie Chart
What types of chart can be used to display categorical data?
Pie Chart
A study was conducted to examine a possible relationship between hours of sleep and income of the employees at a company. What type of classification is this?
Quantitative to quantitative
Which of the following distributions will have a mean that is greater than the median?
Right-skewed distribution
Researchers conducted a biased study trying to determine if there is a relationship between a customer's age and their satisfaction with their service plan. They randomly selected 175 of their first-year customers and asked them to rate their satisfaction as "Very Dissatisfied" , "Dissatisfied" , "Satisfied" , or "Very Satisfied." Where is the misalignment that caused the bias?
Sampling first-year customers.
What type of graph would you use for a Q - Q
Scatterplots
What type of graph would you use for C - Q
Side by side box plots
A marketing researcher was investigating residential water usage in a metropolitan area for a report she was putting together for a client. They polled individual households and asked them to report their average monthly water bill rounded to the nearest dollar. The lowest average monthly water bill was $41 and the highest average monthly water bill was $93. When presenting the data, they wanted every dollar amount to be shown. What display would you suggest she use?
Stem Plot
Data from a study of unemployment rate shows a correlation of r=0.84 between unemployment rate and crime rate, as demonstrated below. What can be concluded about the relationship between unemployment rate and crime rate?
There is a positive association between unemployment rate and crime rate.
Subjects are randomly assigned to two groups. Each group is placed on a special diet plan; a low-fat diet, and a regular diet. After 8 months, the Body Mass Indexes (BMI) of those with the low-fat diet were significantly lower than those with a regular diet.
There is an association between diet and BMI, but not causal relationship can be concluded.
A study shows that there is a positive relationship between a student's confidence before a test and the student's score on the test. A correlation coefficient of 0.78 was found. What can be concluded about this study?
There is an association, but the student's time spent studying may be a lurking variable.
A researcher is studying the effects of sleep on blood pressure. Subjects were randomly divided into two groups. One group was permitted 5 hours of sleep each night for two weeks. The other group was allowed to sleep at least 8 hours each night for two weeks. The blood pressures of both groups were taken at the end of the two weeks and compared and the group with at least 8 hours of sleep each night had significantly lower blood pressure than those with only 5 hours of sleep each night. What conclusion can be made?
This is an experimental study design and not obviously biased.
What type of graph would you use for C - C?
Two-way frequency table
There are 8 blue, 4 green, and 12 red marbles in a bag. One marble is selected from the bag at random. How likely is it that the marble is green?
Unlikely
A social media site wants to know if there is a relationship between age and the number of "likes" a person gives on its site. They send out emails to all users of the site requesting people to participate in a research study on this topic. The sample is made up of all people who respond to the email agreeing to participate. Is there any potential bias?
Yes, because they used a voluntary sample.
Average number of button presses by a visitor is a____ variable.
quantitative
In a Right-skewed (Positively skewed) distribution, the mean tends towards the ____ while the median tends towards the _____ so that the mean has a larger x-value than the median.
right, middle
