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GRE Subject Test: Math : Z-Distribution

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

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Example Questions

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:

14.37

2.3

1.7

1.5

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 : Z Distribution

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:

2.8

3.6

1.7

-3.6

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

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:

1.3

0.66

-14.3

14.6

-0.6

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

Natalie took her university placement examinations in Spanish and math. In Spanish, she scored 82; in math, she scored 86. The results of the Spanish exam had a mean of 72 and a standard deviation of 8. The results of the math exam had a mean of 68 and a standard deviation of 12. On which exam did Natalie do better, compared with the rest of her peers taking these placement exams?

Possible Answers:

The Math exam

The Spanish exam

She did equally well on both exams

None of the other answers, as z-scores cannot be calculated for this question

Correct answer:

The Math exam

Explanation:

We need to calculate Natalie's z-scores for both her Spanish and math exams. Calculating z-scores is as follows:

$\small z=\frac{x-\bar{x}}{s}$

Her z-score for the Spanish exam is $\small \frac{82-72}{8}$ , which equals 1.25, while her z-score for the math exam is $\small \frac{86-68}{12}$ , which equals 1.50. Since both z-scores are positive, Natalie did above average on both tests, but since her z-score for the math exam is higher than her z-score for the Spanish exam, Natalie did better on her math exam when compared to the rest of her peers taking the exam.

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

This year's harvest, the apples had a mean mass of 102g with a standard deviation of . You pick an apple from the harvest and find its mass to be 111g .

What is the z-score of the apple you picked?

Possible Answers:

1.5

0.4

Correct answer:

Explanation:

To find the z-score, we follow the formula

$z=\frac{x-\mu }{\sigma }$ where is the given value, $\mu$ is the mean, and $\sigma$ is the standard deviation.

For this problem we see that

x=111

$\mu = 102$ and

$\sigma =9$

Substituting for these values we see

$z=\frac{111-102 }{9 } =1$

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Example Question #112 : Other Topics

A bread maker has an average life of 9 years, with a variance of 4 years. What is the z-score associated with the probability that a bread maker lasts less than 13 years?

Possible Answers:

Correct answer:

Explanation:

$z=\frac{X-\mu }{\sigma }$

$\mu$ is the average life of the bread maker, in this problem 9 years.

$\sigma$ is the standard deviation of the break makers life. The standard deviation is the square root of the variance.

$\sigma=\sqrt{4}=2$

X is the test statistic we are looking to find. In this problem it is the probability that the bread maker lasts less than 13 years.

$z=\frac{13-9 }{2}=\frac{4}{2}=2$

If you were to find the value associated with a z-score of 2 on the z-table, you would see that

$Pr(X\leq 13)=.9973$

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GRE Subject Test: Math : Z-Distribution

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

All GRE Subject Test: Math Resources

Example Questions

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 : Z 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 : How To Find Z Scores For A Data Set

Example Question #112 : Other Topics

All GRE Subject Test: Math Resources

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