# GRE Subject Test: Math : Probability & Statistics

## Example Questions

### Example Question #11 : Permutations

people are at a farewell party. At the end of the night, each person shakes hands. How many handshakes are made?

NOTE: No two people can shake hands more than once.

Explanation:

Step 1: Determine how many people are there..
There are  people.
Step 2: Determine how many people shake hands in a handshake...
people make one handshake.
Step 3: Determine how many handshakes can be made...
We have a restriction here, so we need to use permutation..

So, there will be  handshakes.

handshakes

### Example Question #16 : Permutations

In how many ways can I rearrange the letters in the word "ANACONDA"?

Explanation:

Step 1: Count how many letters are in the word ANACONDA...

There are 8 letters.

Step 2: Count how many repeats of any letters (if any)..

There are  A's and  N's.

Step 3: Find how many ways I can rearrange...

### Example Question #11 : Permutations

How many ways can I arrange the letters in the word ?

Explanation:

Step 1: Count how many numbers are in the word...

There are  letters.

Step 2: Count the number of repeated letters...

There are  T's

There are  O's

There are  R's

Step 3: To find how many ways I can arrange the letters, take the factorial of the total number of letters and divide it by the factorial of how many times a certain letter repeats...

So,

### Example Question #1 : Uniform Distribution

X is a continuously and uniformly distributed on the interval (0,50). Find the Expected Value (E[x]) and Variance (Var(x)) of X.

Explanation:

Because x is a continuous uniform random variable the expected value and variance can be found with the following formulas:

X is uniform on (a,b). In this case a is 0 and b is 50. Plugging the values of a and b into the given formulas will give the answers:

### Example Question #1 : Binomial Distribution

A fair coin is tossed 15 times. What is the probability of observing less than 3 heads?

Explanation:

This problem uses the Binomial Distribution:

For this problem n is the number of trials, or 15. Because the problem stated that the coin was a fair coin the probability of heads is one half, or .5.

The binomial distribution is a discrete distribution so the expression x<3 has to be broken down.

### Example Question #1 : How To Find Z Scores For A Data Set

The average score on the statistics final exam was 85 and the standard deviation was . Chris scored a . Chris scored higher than what percent of his class?

Explanation:

The first step in this problem is calculating the z-score.

The next step is to look up 4 in the z-table. The value from the table is .

### Example Question #1 : How To Find Z Scores For A Data Set

What is the -score for a value of 115 when the mean of the population is 103 and the standard deviation is 8?

Explanation:

-score indicates whether a particular value is typical for a population or data set.  The closer the -score is to 0, the closer the value is to the mean of the population and the more typical it is.  The -score is calculated by subtracting the mean of a population from the particular value in question, then dividing the result by the population's standard deviation.

### Example Question #1 : How To Find Z Scores For A Data Set

A population of values has a mean of 43 and a standard deviation of 12.  One of the values in the population is 49.  What is the Z-score for that value?

Explanation:

A Z-score indicates whether a particular value is typical for a population or data set.  The closer the Z-score is to 0, the closer the value is to the mean of the population and the more typical it is.  The Z-score is calculated by subtracting the mean of a population from the particular value in question, then dividing the result by the population's standard deviation.

### Example Question #2 : How To Find Z Scores For A Data Set

The z-score is also known as the standard score.

The average temperature for all the days preceding the last for the month of February was 55 degrees Farhenheit, with a standard deviation of 5 degrees.

On the last day, the temperature was 73 degrees F. What is the z-score for the temperature on the last day?

Explanation:

To find the z-score, follow the formula

or

### Example Question #2 : How To Find Z Scores For A Data Set

A population has a standard deviation of  and a mean of . One of the values in the population is .  What is the z score for that value?