Discrete RV
Continuous RV
Probability
Displaying Data
Miscellaneous
100
The random variable X represents the number of pets owned by a randomly selected family. What is the probability that a randomly chosen family has 3 or more pets?
.25
100
A subway train arrives at a particular station every 10 minutes. Passengers arrive at the station at random times throughout the 10-minute interval between trains. Let (X) represent the waiting time, in minutes, for a randomly selected passenger. Assume (X) follows a uniform distribution from 0 to 10 minutes.
Calculate the probability that a randomly selected passenger waits more than 3 minutes and interpret your answer in context.
P(X>3)= .7
There is a 70% probability that after many, many trials a randomly selected passenger will wait more than 3 minutes for the next subway train.
100
At a high school, 60% of students participate in a sport, 35% participate in a school club, and 20% participate in both a sport and a club. One student is selected at random. Calculate the probability that a student is in a sport or a club.
.6+.35-.2= .75
100
A school surveys 200 students about their favorite school lunch: pizza, tacos, chicken sandwiches, or pasta. The principal wants to compare how many students chose each lunch option.
bar graph
100
A researcher wants to survey students at a high school about their homework habits. The researcher separates students into freshmen, sophomores, juniors, and seniors. A random sample of 25 students is selected from each grade level. What type of sampling method is used.
stratified random sampling
200
Students were asked to read books over the summer. Let X represent the number of books read by a randomly selected student. What is the expected value of book read. Interpret your answer in context.
0(.12)+1(.28)+2(.25)+3(.26)+4(.09)=1.92
The average number of books read after the long run of selecting many, many students is 1.92 books.
200
Test scores at a school are approximately normally distributed with a mean of 80 points and a standard deviation of 6 points.
Calculate the probability that a randomly selected student scores less than 86?
normaldist(0,1)
P(z<1)=.8413
200
A basketball player makes 70% of free throws. Assume each free throw is independent of the others. Calculate the probability that the player makes both of the next two free throws.
.7 * .7 = .49
200
A teacher records the scores of 30 students on a statistics test. The teacher wants to examine the distribution's shape, center, spread, and possible outliers.
histogram
200
A researcher wants to know what people think about a new clothing store. The researcher surveys people who happen to be walking past the store's entrance. What type of sampling is used?
convenience sampling
300
A carnival game costs $2 to play. Let X be the possible amount you can win. Is this game favorable to the player? Justify your answer.
(-2)(.6)+(2)(.2)+5(.15)+(10)(.05)= $.45
yes, the expected value is positive.
300
The weights of male cocker spaniels are approximately normally distributed with a mean of 34 pounds and a standard deviation of 2 pounds.
What is the probability that a male cocker spaniel weighs between 30 and 35 pounds.
normaldist(34,2)
P(30<x<35) = .6687
300
A teacher has 12 students who volunteer to help with a school event. Seven are seniors and five are juniors. The teacher randomly selects two different students without replacement.
Calculate the probability that both selected students are seniors.
(7/12) x (6/11) = .318182
300
A researcher surveys 150 adults and records whether each person exercises regularly (yes or no) and whether each person gets at least 8 hours of sleep (yes or no). The researcher wants to investigate the association between these two categorical variables.
two way table
300
A teacher randomly assigns 90 students to one of three study methods: rereading notes, using flashcards, or taking practice quizzes. After one week, all students take the same test, and their scores are recorded. Identify the following:
A) explanatory variable
B) response variable
C) treatments
A) one of the 3 study methods used
B) score on the test
C) rereading notes, using flashcards, taking practice quizzes
400
A soccer team scores from 0-5 goals in any given game. Let X be the number of goals scored in a game. A statistician found that the expected mean is 1.5 goals and the standard deviation is .8 goals. Interpret the standard deviation of X.
The number of goals scored by the team typically varies by .8 goals from the mean of 1.5 goals.
400
Race times for high school boys 1600 meter State Championship race is normally distributed with a mean time of 4.22 minutes (262 seconds) and a standard deviation of 6 seconds. What would a high school boy need to run in order to be in the top 10%?
normaldist(262,6) bounds
P(x<254.3107)=.1 or 4.23 minutes
400
A soccer player makes 85% of her penalty kicks. She plans to take 4 kicks. What is the probability that she makes at least one?
1- p(making none)
1-(.15)^4 = .999494
400
Two statistics classes take the same exam. The teacher wants to compare the distributions of their test scores, including their medians, variability, and possible outliers.
parallel box plots
400
A researcher wants to compare the effectiveness of two different pain-relief creams. She suspects that a person's age may affect how quickly the cream works. The researcher recruits 40 volunteers and divides them into two blocks based on age: adults under 40 and adults 40 or older. Within each block, the researcher randomly assigns half of the volunteers to receive Cream A and the other half to receive Cream B. All volunteers apply their assigned cream after completing the same exercise routine. The researcher then measures how long it takes for each volunteer's muscle soreness to decrease. Describe the following:
A) Experimental design used
B) Identify the subjects in this experiment.
C) Identify the treatments.
D) Identify the response variable.
A) randomized block design
B) 40 volunteers
C) Using Cream A or using Cream B
D) time it takes for muscle soreness to decrease
500
Let X represent the number of times a randomly selected student is tardy to class on any given day of school. A admin wants to take the data and put it in a histogram to present at the next staff meeting. Describe the shape of the histogram.
unimodal and skewed to the right
500
A shipping company tracks the delivery times for packages sent from one of its distribution centers. The delivery times are approximately normally distributed, with a mean of 42 hours and a standard deviation of 6.5 hours.
The company opens a second distribution center. Delivery times from this center are approximately normally distributed, with a mean of 39 hours and a standard deviation of 4 hours.
A package from each center is randomly selected. Which package delivery time is more unusual for its distribution: a delivery time of 50 hours from the first center or a delivery time of 46 hours from the second center? Justify your answer.
N(42,6.5)
z=(50-42)/6.5 = 1.23
N(39,4)
z=(46-39)/4 = 1.75
The delivery time for the second distribution center is more unusual because its z-score of 1.75 is farther from the mean compared to the z-score of the first distribution center of 1.23.
500
A school surveyed 300 students about whether they have a part-time job and whether they participate in a school sport. The results are shown in the table below. Are the events “has a part-time job” and “plays a school sport” independent? Justify your answer using probabilities.
P(sport) = 15/300 = .5
P(sport|job) = 45/120 = .375
.5 is not equal to .375 so they are not independent
500
A teacher records the number of AP classes taken by their 25 students. The teacher wants to see individual values, clusters, gaps, and possible outliers.
dotplots
500
A researcher wants to investigate whether listening to music while studying affects students’ test scores. The researcher asks for volunteers from a nearby high school to participate in the study. Thirty students volunteer, and the researcher divides them into two groups by randomly assigning each student to one of two conditions: listening to instrumental music while studying or studying in silence. After studying for 30 minutes, all students take the same test, and their scores are recorded.
What conclusions can we make?
random selection - no so we cannot generalize to entire population
random assignment - yes so we say there is causation