Statistical Patterns and Random Phenomena
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AP Statistics › Statistical Patterns and Random Phenomena
Let us suppose we have population data where the data are distributed Poisson
(see the figure for an example of a Poisson random variable). 
Which distribution increasingly approximates the sample mean as the sample size increases to infinity?
Normal
Poisson
Exponential
Gamma
Explanation
The Central Limit Theorem holds that for any distribution with finite mean and variance the sample mean will converge in distribution to the normal as sample size 
When rolling a 6 sided dice, what is the probability of rolling a 2 or a 4?
Explanation
In the single roll of a dice, rolling a 2 is mutually exclusive of rolling a 4. When a question asks for the probability of event A "or" event B, the probability is the sum of each event.
First, find the probability of each individual event.
Because the problem asks for a 2 OR a 4, add the indivual probabilities together.
Which of the following is a discrete random variable?
The number of times heads comes up on 10 coin flips
The amount of water that passes through a dam in a random hour
The rate of return on a random stock investment
The length of a random caterpillar
Explanation
A discrete variable is a variable which can only take a countable number of values. For example, the number of times that a coin can come up heads in ten flips can only be 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, or 10. Thus, there are a countable number of possible outcomes (in this case 11). This is true for coin flips, but not for caterpillar length, water flow, or rates of return for stocks.
In a particular library, there is a sign in the elevator that indicates a limit of 
If a random sample of 
None of the other answers
Explanation
This question deals with the Central Limit Theorem, which states that a random sample taken from a large population where the sampling distribution of sample averages is approximately normal has a standard deviation equal to the standard deviation of the population divided by the square root of the sample size. The information given allows us to apply the Central Limit Theorem as it satisfies the necessary characteristics of the sampling distribution/size. The standard deviation of the population is 27lbs, and the sample size is 36; therefore, the standard deviation of the 36-person random sample is 
Which of the following is a discrete random variable?
The number of times heads comes up on 10 coin flips
The amount of water that passes through a dam in a random hour
The rate of return on a random stock investment
The length of a random caterpillar
Explanation
A discrete variable is a variable which can only take a countable number of values. For example, the number of times that a coin can come up heads in ten flips can only be 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, or 10. Thus, there are a countable number of possible outcomes (in this case 11). This is true for coin flips, but not for caterpillar length, water flow, or rates of return for stocks.
Which of the following is a discrete random variable?
The number of times heads comes up on 10 coin flips
The amount of water that passes through a dam in a random hour
The rate of return on a random stock investment
The length of a random caterpillar
Explanation
A discrete variable is a variable which can only take a countable number of values. For example, the number of times that a coin can come up heads in ten flips can only be 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, or 10. Thus, there are a countable number of possible outcomes (in this case 11). This is true for coin flips, but not for caterpillar length, water flow, or rates of return for stocks.
In a particular library, there is a sign in the elevator that indicates a limit of
If a random sample of
None of the other answers
Explanation
This question deals with the Central Limit Theorem, which states that a random sample taken from a large population where the sampling distribution of sample averages is approximately normal has a standard deviation equal to the standard deviation of the population divided by the square root of the sample size. The information given allows us to apply the Central Limit Theorem as it satisfies the necessary characteristics of the sampling distribution/size. The standard deviation of the population is 27lbs, and the sample size is 36; therefore, the standard deviation of the 36-person random sample is
Assume there is an election involving three parties: D, R, and I. The probability of D winning is .11, R winning is .78, and I winning is .11. What is the probability of D or R winning?
.89
.78
1
0
Explanation
Since all of the events are mutually exclusive (one of the parties must win), you can get the probability of either D or R winning by adding their probabilities.
Since the probability of D winning is .11 and R winning is .78, the probability of D or R winning is .89.
Students collected 150 cans for a food drive. There were 23 cans of corn, 48 cans of beans, and 12 cans of tomato sauce. If a student randomly selects one can to give away, what is the probability that the can will be either tomato sauce or beans?
Explanation
In this case, we want to know the probability of multiple, mutually exclusive possible outcomes. The possible outcomes are mutually exclusive because one can of food could not be both beans and tomato sauce. To determine the probability of the two possible outcomes, add them together and then find the least common denominator.
When rolling a 6 sided dice, what is the probability of rolling a 2 or a 4?
Explanation
In the single roll of a dice, rolling a 2 is mutually exclusive of rolling a 4. When a question asks for the probability of event A "or" event B, the probability is the sum of each event.
First, find the probability of each individual event.
Because the problem asks for a 2 OR a 4, add the indivual probabilities together.