Distributions
Define SUCS
Shape Unusual Center Spread
The 68-95-99.7% rule is also known as the *** rule
Empirical
If two events are independent, then P(A|B)= ?
P(A)
A marketing survey compiled data on the number of personal computers in households. If X = the number of computers in a randomly-selected household, and we omit the rare cases of more than 5 computers, then X has the following distribution:
X 0 1 2 3 4 5
P(X) 0.24 0.37 0.20 0.11 0.05 0.03
What is the probability that a randomly chosen household has at least two personal computers?
0.20 + 0.11 + 0.05 + 0.03 = 0.59
A factory overseer selects 404 threaded rods at random from those produced that week at the factory, then she tests their tensile strength.
Identify the population and sample in this setting.
The population is threaded rods produced at the factory that week; the sample is the 404 threaded rods selected.
The population is the entire group of people or things we want to study.
The sample is the part of the population that we actually collect data from.
What is a distribution with only one major peek called?
Unimodel
What's another name for a cumulative frequency graph?
Ogive
A fair coin comes up tails 4 times in a row. What is the probability that the coin will come up heads on the next flip?
50%
A large bakery uses a machine to dispense frosting onto its cookies. A certain type of cookie gets 4 dots of frosting on top of each cookie. The dots of frosting have a mean mass of μ = 3 grams and a standard deviation of σ = 0.25 grams. We can assume that the masses of the dots of frosting are independent from each other. Let T be the total mass of the dots of frosting on a randomly chosen cookie. What is μT?
Security workers at an airport randomly choose one of the first 50 people to pass through a checkpoint for extra security screening. After that person, they choose every 50th person who passes through for extra screening as well. What kind of sample is this?
Systematic random sample
How do you calculate IQR
Q3 - Q1
How do the shape, center, and spread change when you add/subtract the same value to every score?
shape: unchanged
center: add/subtract the same value
spread: unchanged
What is the difference between two disjoint events and two independent events?
Disjoint means the events cannot occur at the same time (there is no intersection). Independent means the outcome of one event won't affect the outcome of the other.
Casey ran out of time while taking a multiple-choice test and plans to guess on the last 10 questions. Each question has 5 possible choices, one of which is correct. Let X = the number of answers Casey correctly guesses in the last 10 questions.
Find P(X=2)
(10 2) (1/5)^2 * (4/5)^8
A prestigious university wants to estimate the average starting salary of its graduates. The alumni outreach department sends an email to the most recent address they have on file for every graduate. The email asks the graduates to participate in a survey about their employment history and starting salary.
Which of the following is not a legitimate concern about their survey results being representative of all graduates?
A) Some graduates may no longer check the email address that the university has on file.
B) Graduates might claim their salary is higher than it really is, but relatively few would report a salary lower than what it really is.
C) Current students are not included in the sample.
D) Unemployed graduates may choose to not participate in the survey.
E) Some graduates may not want to share that type of personal information with the university.
C; The goal of survey is to estimate the average starting salary of graduates, there's no reason to include current students in the sampling frame.
How do you test for an outlier?
Must fall more than 1.5 X IQR above the third quartile or below the first quartile
What does NPP stand for?
Normal Probability Plot
If P(A)=0.18, P(B)=0.41, and P(A∩B)=0.24, then what is P(A∪B)?
P(A∪B) = P(A) + P(B) - P(A∩B) = 0.18 + 0.65 - 0.24 = 0.59
Ravi sells real estate. Based on previous data, he knows that 5%, percent of home tours result in a sale. Assume that the results of these tours are independent from each other.
Which of the following choices are binomial random variables? (could be more than 1 right answer)
A) Take a random sample of 3 tours and let K = the number of tours that result in a sale.
B) Take a random sample of 3 tours and let M = equal the amount of sales (in dollars) generated by the tours.
C) Take a random sample of 30 tours and let L = equal the number of tours that result in a sale.
A and C are correct
A is correct because : Each trial has two outcomes (sale or not), results of each trial are independent, there is a fixed number of trials (3), and the probability of success is the same for each trial (5%).
B is wrong because : M isn't binomial since each tour is being recorded as a number that isn't being categorized as a success or failure
C is also correct because : Each trial has two outcomes (sale or not), results of each trial are independent, there is a fixed number of trials (30), and the probability of success is the same for each trial (5%).
A gym that specializes in weight loss offers its members an optional dietary program for an extra fee. To study the effectiveness of the dietary program, a manager at the gym takes a random sample of 50 members who participate in the dietary program and 50 members who don't. The manager finds that those who participated in the dietary program, on average, lost significantly more weight than those who didn't participate in the program in the past 3 months.
The manager concludes that the dietary program caused the increased weight loss for the gym's members during that time period.
What is a confounding variable that makes their conclusion inappropriate?
A) The lack of replication to other time periods
B) The lack of attention to the placebo effect
C) The members' choice of whether or not they participated in the dietary program
D) The exclusion of nonmembers in the study
E) The random samples of 50 members
C; The manager's study lacked random assignment. The members who chose to be in the dietary program paid an extra fee, so they may be more motivated in general to lose weight.
There are three children in a room, ages three, four, and five. If a four-year-old child enters the room, what would happen to the mean and variance?
Mean age will stay the same but the variance will decrease
What are both of the important features of a density curve?
1. area under curve has to equal 1
2. all of it is above or on the horizontal axis
According to the National Telecommunication and Information Administration, 56.5% of U.S. households owned a computerbin 2001. What is the probability that of three randomly selected U.S. households at least one owned a computer in 2001.
P(at least 1 household owns computer) = 1 - P(none own computer) = 1 - P(.435)3 = .918 or 91.8%
Jeremiah makes 25% of the three-point shots he attempts. For a warm up, Jeremiah likes to shoot three-point shots until he successfully makes one. Let M be the number of shots it takes Jeremiah to successfully make his first three-point shot. Assume that the results of each shot are independent.
Find the probability that Jeremiah's first successful shot occurs on his 3rd attempt.
The answer is : 0.140625
A car manufacturer created a new voice-control system that allows drivers to have limited use of their phones while keeping both hands on the wheel. They want to know if the system results in drivers making fewer mistakes, so they recruit volunteers for an experiment.
Each subject is randomly assigned to one of three groups: voice-controlled phone use, regular phone use, or no phone use at all. Subjects drive the same simulated course while researchers send notifications at set moments to the drivers who can use phones. The researchers will then compare how many mistakes are made between the groups.
What is the primary purpose of including a group who doesn't use a phone at all?
A) To ensure subjects are blind as to which treatment group they are in
B) To reduce the impact of the placebo effect
C) To utilize a randomized blocked design
D) To form a matched pair with the group that uses voice-control
E) To serve as a control group for comparison
E; Comparing the voice-control group to the regular phone use group is useful for seeing if voice-control is safer than regular use. Including a group that doesn't use a phone at all is useful for seeing if voice-control is just as safe as no phone use.