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GRE Subject Test: Math : Probability & Statistics

Study concepts, example questions & explanations for GRE Subject Test: Math

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2 Diagnostic Tests 148 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #15 : 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.

Possible Answers:

Correct answer:

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 11P2 handshakes.

$11P2=\frac {11*10}{2*1}=11*5=55$ handshakes

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Example Question #53 : Combinational Analysis

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

Possible Answers:

4000

3830

3360

3000

Correct answer:

3360

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...

$\frac {8!}{3!*2!}=\frac {8*7*6*5*4*3*2*1}{3*2*1*2*1}...$

$...=\frac {8*7*6*5*4}{2}=8*7*6*5*2=3360$

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Example Question #52 : Combinational Analysis

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

Possible Answers:

$\frac {12!}{2!\times2!\times2!}$

$\frac {12!}{2!\times2!\times3!}$

{12!}

${2!\times2!\times2!}$

Correct answer:

$\frac {12!}{2!\times2!\times2!}$

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, $\frac {12!}{2!\times2!\times2!}$

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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.

Possible Answers:

E[x]=25

Var(x)=208.33

E[x]=4.167

Var(x)=208.33

E[x]=4.167

Var(x)=1250

E[x]=25

Var(x)=2500

E[x]=25

Var(x)=200.166

Correct answer:

E[x]=25

Var(x)=208.33

Explanation:

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

$E[x]=\frac{a+b}{2}$

$Var(x)=\frac{(b-a)^2}{12}$

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:

$E[x]=\frac{a+b}{2}=\frac{0+50}{2}=25$

$Var(x)=\frac{(b-a)^2}{12}=\frac{2500}{12}=208.33$

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Example Question #1 : Binomial Distribution

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

Possible Answers:

0.0032

0.125

0.0139

0.0037

0.5

Correct answer:

0.0037

Explanation:

This problem uses the Binomial Distribution: $\binom{n}{k}p^k(1-p)^{n-k}$

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.

Pr(x< 3)=Pr(x=0)+Pr(x=1)+Pr(x=2)

$Pr(x=0)=\begin{pmatrix} 15\\0 \end{pmatrix} (.5)^0(1-.5)^{15}=.000031$

$Pr(x=1)=\begin{pmatrix} 15\\1 \end{pmatrix} (.5)^1(1-.5)^{14}=.00046$

$Pr(x=2)=\begin{pmatrix} 15\\2 \end{pmatrix} (.5)^2(1-.5)^{13}=.0032$

Adding the probabilities will give the final answer.

.000031+.0046+.0032=.0037

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

The average score on the statistics final exam was 85 and the standard deviation was 2.5 . Chris scored a . Chris scored higher than what percent of his class?

Possible Answers:

95.7

Correct answer:

Explanation:

The first step in this problem is calculating the z-score. $z=( x-\mu)/\sigma$

(95-85)/2.5= 4

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

$1-.0000317\: is \: .9999683.$

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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?

Possible Answers:

2.3

1.5

14.37

1.7

Correct answer:

1.5

Explanation:

A -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.

$z=\frac{X-\bar{X}}S{}$

(115-103)/8=1.5

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Example Question #1 : Z Distribution

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?

Possible Answers:

0.8

-0.8

0.05

0.5

Correct answer:

0.5

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.

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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?

Possible Answers:

3.6

-3.6

1.7

2.8

Correct answer:

3.6

Explanation:

To find the z-score, follow the formula

$z=\frac{x-\mu}{\sigma }, x=score, \mu=mean, \sigma=S.D.$

$z=\frac{73-55}{5}$

z=3.6

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Example Question #1 : Data Sets And Z Scores

A population has a standard deviation of 3.5 and a mean of 17.2 . One of the values in the population is 19.5 . What is the z score for that value?

Possible Answers:

0.66

1.3

-0.6

14.6

-14.3

Correct answer:

0.66

Explanation:

A z score is unique to each value within a population.

To find a z score, subtract the mean of a population from the particular value in question, then divide the result by the population's standard deviation.

$z=\frac{x-\mu}{\sigma}=\frac{19.5-17.2}{3.5}= \frac{2.3}{3.5}=0.6571$

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GRE Subject Test: Math : Probability & Statistics

Study concepts, example questions & explanations for GRE Subject Test: Math

All GRE Subject Test: Math Resources

Example Questions

Example Question #15 : Permutations

Example Question #53 : Combinational Analysis

Example Question #52 : Combinational Analysis

Example Question #1 : Uniform Distribution

Example Question #1 : Binomial Distribution

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

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

Example Question #1 : Z Distribution

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

Example Question #1 : Data Sets And Z Scores

All GRE Subject Test: Math Resources

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