1105 Probability and Statistics Exam 2 Practice Quiz Part 2
Describe how the Fundamental Counting Principle can be used to count how many ways a sequence of events can occur
Use the fundamental counting principle to determine how many ways you can choose a shirt and pants to wear if you own a green, blue, gray, and white shirt, and tan, blue, or black pants (One item of clothing per color).
12
4
3
6
What is the difference between a combination and a permutation?
A combination is a specific order of objects/elements, whereas a permutation is a collection of specific objects/elements
A permutation is a specific ordering of objects/elements, whereas a combination is an unordered collection of specific objects/elements.
You have a desk, a chair, a bed, a dresser, a lamp, and a hamper you want to place in your room, but only room to place four of these things in your room. How many ways can you arrange these pieces of furniture in your room?
360
15
24
96
How many ways can you pick 10 college students out of a group of 20 to try to fit into a telephone booth?
184,756
200
~670 Billion
2924
What is a random variable?
The numerical outcome of an experiment
A numeric description of the outcome of an experiment
A variable used in experiments that are truly random rather than pseudo-random
An experimental value that is generated by random chance.
I conduct an experiment in which I measure the weight of the average house pet. Is this weight a discrete or a continuous random variable?
Continuous
Discrete
Select all necessary conditions for a function to be a probability distribution
p(x) is nonnegative for any x
The sum of all p(x) = 1
p(x) is always increasing as x increases
p(x) always produces an integer value
Determine a probability distribution function for X based on the table provided.
p(x) = 1/10
p(x) = x/10
p(x) = x when x > 1/10
p(x) = x/10 when x = 1, 2, 3, or 4. otherwise, p(x) = 0
Calculate the expected value of X for the above distribution
5.02
12
1
Trick question, this is not a valid distribution in the first place
True or False: The Standard Deviation of any distribution is always the square root of its variance.
True
False
Ira ran out of time while taking a multiple-choice test and plans to guess on the last 6 questions. Each question has 4 possible choices, one of which is correct. Let X = the number of answers Ira correctly guesses in the last 6 questions. What is the probability that Ira gets less than 2 questions correct? You may use the table provided rather than calculate the probability by hand if you like.
2.2
.167
.143
.534
Which two properties are true of the Poisson Distribution?
It is always true that the probability of at least one successful outcome in a Poisson distributon is twice the standard deviation
The expected value of a Poisson Distribution can be negative
The probability of X taking on a specific value is the same for any two intervals of length?
The probability of occurrence in one interval is independent of the occurrence in any other interval
Given a uniform distribution function, what is the probability P(X = 30)?
1
0
30
.3
Consider a uniform distribution where the reasonable values of X range from 47 to 77. What is the probability that X is less than 52 but at least 49?
.03
.30
.1
.7
Why does converting X values to z values still allow us to solve questions about probabilities of X?
If you have a normal distribution with mean = 11, and standard deviation = 2, what is the probability that your value of X is greater than or equal to 15?
How does the answer to the previous question relate to the empirical rule we learned about at the beginning of the semester?
What type of distribution function models this question: The average elementary school child takes 15 minutes to eat their lunch. What is the probability that a child eats their lunch in 5 minutes or less?
Poisson Distribution
Normal Distribution
Discrete Distribution
Exponential Distribution
Calculate probability mentioned in the question listed above. Write your answer as a decimal rounded to three places.
For an exponential distribution, what is the probability that a random variable takes on a range of values that are entirely negative?
0
1
.5
.25
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