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Algebra II : Algebra II

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #1 : Z Scores

In a normal distribution, if the mean score is 8 in a gymnastics competition and the student scores a 9.3, what is the z-score if the standard deviation is 2.5?

Possible Answers:

-1.04

2.16

-0.85

0.52

0.85

Correct answer:

0.52

Explanation:

Write the formula to find the z-score. Z-scores are defined as the number of standard deviations from the given mean.

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

Substitute the values into the formula and solve for the z-score.

$z=\frac{x-\mu}{\sigma } = \frac{9.3-8}{2.5} =0.52$

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Example Question #1 : Z Scores

Suppose a student scored a on a test. The mean of the tests are , and the standard deviation is . What is the student's z-score?

Possible Answers:

-2.475

-0.875

-0.75

-0.85

-1.143

Correct answer:

-0.875

Explanation:

Write the formula for z-score where is the data, $\mu$ is the population mean, and $\sigma$ is the population standard deviation.

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

Substitute the variables.

$z=\frac{65-72}{8} =- \frac{7}{8} = -0.875$

The z-score is: -0.875

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Example Question #2 : Z Scores

Suppose Bob's test score is 50. Determine the z-score if the standard deviation is 3, and the mean is 75.

Possible Answers:

$-\frac{25}{3}$

$-\frac{75}{47}$

$-\frac{25}{6}$

$-\frac{2}{3}$

Correct answer:

$-\frac{25}{3}$

Explanation:

Write the formula for z-scores. This tells how many standard deviations above the below the mean.

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

Substitute the known values into the equation.

$z=\frac{50-75}{3} =-\frac{25}{3}$

The z-score is: $-\frac{25}{3}$

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Example Question #1 : Z Scores

Find the z-score if the result of a test score is 6, the mean is 8, the standard deviation is 2.

Possible Answers:

$\textup{The answer is not given.}$

Correct answer:

Explanation:

Write the formula to determine the z-scores.

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

Substitute all the known values into the formula to determine the z-score.

$z=\frac{6-8}{2}$

Simplify this equation.

$z=\frac{-2}{2} = -1$

The answer is:

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Example Question #11 : Z Scores

Determine the z-score of a test result is 45, the mean is 60, and the standard deviation is 8.

Possible Answers:

$-\frac{15}{64}$

$-\frac{15}{16}$

$\frac{1}{8}$

$\textup{There is not enough information to determine the z-score.}$

$-\frac{15}{8}$

Correct answer:

$-\frac{15}{8}$

Explanation:

Write the formula for z-scores. Z-scores determine the number of standard deviations below or above the mean.

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

Substitute the values into the formula to determine the z-score.

$z=\frac{45-60}{8}= -\frac{15}{8}$

The z-score is $-\frac{15}{8}$ .

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Example Question #12 : Z Scores

Suppose Billy scored a 54 on his exam. The mean of the exam grades is 66 and the standard deviation is 3. What is the z-score?

Possible Answers:

-3.75

Correct answer:

Explanation:

Write the formula for z-scores. Z scores determine how many standard deviations a score is above or below the mean.

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

Substitute the known values in order to determine the z-score.

$z=\frac{X-\mu}{\sigma} = \frac{54-66}{3} = -4$

The answer is:

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Example Question #11 : Graphing Data

Sarah scored an 8.5 out of ten on her gymnastics floor routine. If the mean of the scores is 9.2 and the standard deviation is 1.3, what is her z-score?

Possible Answers:

-0.642

-0.574

-0.538

-1.268

0.338

Correct answer:

-0.538

Explanation:

Write the formula for z-scores. Z-scores are indicators of how many standard deviations above or below the mean.

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

$x=\textup{score}$

$\mu = \textup{mean}$

$\sigma =\textup{ standard deviation}$

Substitute the known values.

$z=\frac{8.5-9.2}{1.3} = \frac{-0.7}{1.3} = -0.538$

The answer is: -0.538

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Example Question #11 : Z Scores

You just took your ACT. The mean score was a with a standard deviation of . If you scored a , what is your z-score?

Possible Answers:

0.75

1.55

1.33

1.25

Correct answer:

1.33

Explanation:

Use the formula for z-score:

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

Where is your score, $\mu$ is the mean, and $\sigma$ is the standard deviation.

$z=\frac{26-22}{3}=1.33$

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Example Question #1 : How To Find Direct Variation

varies directly with the square root of . If x = 25 , then y = 48 . What is the value of if x = 81 ?

Possible Answers:

$26\tfrac{2}{3}$

155.52

86.4

491.52

None of these answers are correct.

Correct answer:

86.4

Explanation:

If varies directly with the square root of , then for some constant of variation ,

$\small y = K \sqrt{x}$

If x = 25 , then y = 48 ; therefore, the equation becomes

$\small \small 48 = K \sqrt{25}$ ,

5K = 48 .

Divide by 5 to get K = 9.6 , making the equation

$\small \small y = 9.6 \sqrt{x}$ .

If x = 81 , then $\small \small \small y = 9.6 \sqrt{81} = 9.6 \cdot 9 = 86.4$ .

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Example Question #2 : Variable Relationships

If varies directly with $x^{3}$ and when x=5 , y=61.125 due to the effect of a constant, what is the value of when x=11 ?

Possible Answers:

y=43.331

y=650.859

y=134.475

y=1,331

y=672.375

Correct answer:

y=650.859

Explanation:

Since varies directly with $x^{3}$ , $y=Kx^{3}$ where is a constant.

1. Solve for when x=5 and y=61.125 .

$y=Kx^{3}$

$61.125=K(5^{3})$

$K=\frac{61.125}{125}=0.489$

2. Use your equation to solve for when x=11 .

$y=0.489x^{3}$

$y=0.489(11^{3})=650.859$

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Algebra II : Algebra II

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #1 : Z Scores

Example Question #1 : Z Scores

Example Question #2 : Z Scores

Example Question #1 : Z Scores

Example Question #11 : Z Scores

Example Question #12 : Z Scores

Example Question #11 : Graphing Data

Example Question #11 : Z Scores

Example Question #1 : How To Find Direct Variation

Example Question #2 : Variable Relationships

All Algebra II Resources

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