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Problems
Variables
Binomial Distributions
Geometric Distributions
Equations/ Linear Transformations
100
A business evaluates a venture as follows. It stands to make a profit of $10,000 with probability 3/20, a profit of $5,000 with probability 9/20, to break even with probability 5/20, and to lose $5,000 with probability 3/20. What is the expected profit in dollars?
$3,000 Because (10,000)(.15)+(5000)(.45)+(0)(.25)+(-5,000)((.15)=$3,000 .
100
Takes numerical values that describe the outcome of some chance process.
What is a random variable?
100
What are the conditions for a binomial setting?
1) Binary: Outcomes are either a success or a failure 2) Independent: Trials must be independent 3) Number: Number of trials(n) must be fixed 4) Success: The probability of success must be same for each trial
100
How can you calculate geometric probabilities?
P(Y=k)= (1-p)^(k-1) * (p)
100
Σxipi
What is the equation for calculating the mean (expected value) of a discrete random variable?
200
Let the random variable X represent the profit made on a randomly selected by a certain store. Assume that X is Normal with mean $360 and standard deviation $50. What is P(X>40)? [Hint: Z Table]
What is 0.2119. Because P(x>400)=P(z>((400-360)/50))=P(z>0.8)=0.2119
200
What does the continuous random variable distribution look like?
What is a histogram?
200
What are the possible values of a binomial random variable?
X is between 0 and the number of trials (Whole numbers)
200
What are the conditions for a geometric setting?
1) Probability of success is the same for each trial. 2) No set # of trials
200
z = (x-μ)/σ
What is The probability of a continuous random variable is the area under the curve. How is this calculated?
300
In a large population of college students, 20% of the students have experienced math anxiety. If you take a random sample of 10 students, what is the mean and standard deviation of students in the sample who have experienced math anxiety?
1.265 Because μX=np=(10)(.2)=2; σx=√np(1-p)=√(10)(.2)(.8)= 1.265
300
Takes a fixed set of possible values with gaps in between. Probabilities must be between 0 and 1. Infinite set(sequences)
What is a discrete random variable?
300
What are the parameters of a binomial distribution?
Parameter is n(fixed # of trials) and p(probability of success on any 1 trial)
300
What are the possible values of a geometric random variable?
Number of trials to get a success.
300
E(T) = μX + μY
What is For two random variables x and y, if T = x+y then what is the mean (expected value) of T?
400
A professional soccer player succeeds in scoring a goal on 84% of penalty kicks. Assume that the success of each kick is independent. What is the probability that he scores on five or fewer in the next 10 penalty kicks?
0.0130 Because it is a binomial probability, P(X≤5)=binomcdf(10,0.84,5)=.0130
400
Example of a continuous random variable
What is Amount of Time?
400
How can you calculate binomial probabilities?
binompdf(n,p,k)=> P(X=k) binomcdf(n,p,k)=> P(X less than or equal to k)
400
What are the parameters of geometric distributions?
P: Probability of success on any trial Y: Number of trials for success
400
What is a linear transformation?
When a constant is added to or subtracted from all the data, or when all data are multiplied or divided.
500
Which actor was the voice of Darth Vader in the original Star Wars trilogy?
Who is James Earl Jones?
500
Example of Discrete Random Variable
What is foot length?
500
By law in Russia, where do the homeless have to be after 10 PM?
At home
500
It is illegal in Georgia to do what with a fork?
Eat fried chicken
500
How does a linear transformation affect the mean and standard deviation of a random variable?
Mean: Increases or decreases no matter what Standard Deviation: Stays the same when constant is added, Increase or Decrease when multiplied or divided.