# Algebra II : Graphing Data

## Example Questions

### Example Question #7 : 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?

Explanation:

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

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

### Example Question #8 : 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?

Explanation:

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

Substitute the variables.

The z-score is:

### Example Question #1 : Z Scores

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

Explanation:

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

Substitute the known values into the equation.

The z-score is:

### Example Question #10 : Z Scores

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

Explanation:

Write the formula to determine the z-scores.

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

Simplify this equation.

### 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.

Explanation:

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

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

The z-score is .

### Example Question #11 : 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?

Explanation:

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

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

### Example Question #13 : Z Scores

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?

Explanation:

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

Substitute the known values.

### Example Question #14 : 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?

Explanation:

Use the formula for z-score:

Where  is your score,  is the mean, and  is the standard deviation.

### Example Question #1 : Variable Relationships

varies directly with the square root of . If , then  . What is the value of  if ?

None of these answers are correct.

Explanation:

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

If , then ; therefore, the equation becomes

or

.

Divide by 5 to get , making the equation

.

If , then .

### Example Question #2 : Variable Relationships

If  varies directly with  and when  due to the effect of a constant, what is the value of  when ?

Explanation:

Since  varies directly with  where  is a constant.

1. Solve for  when  and .

2. Use your equation to solve for  when .