WorksheetsFinding z-score
Total questions: 25
Worksheet time: 44mins
If heights of 3rd graders follow a normal distribution with a mean of 52 inches and a standard deviation of 2.5 inches, what is the z score of a 3rd grader who is 47 inches tall?
Find the Z-score.
Mean = 22
Standard Deviation: 3.1
x = 29
2.26
16.45
-2.26
1.26
Find x.
Z-score = -1.4
mean = 29.8
Standard Deviation: 7
20
-39.6
40
-9.8
If I tell you that you scored at the 55th percentile on your final exam, you would know:
55% of the class scored the same or worse than you did
You earned a 55% on the exam
You failed the exam
45% of the class scored worse than you did
Which of the following is a formula that describes calculating a z-score?
Z = (score - mean) / stand. deviation
Z = (mean - score) / stand. deviation
Z = score(stand. dev)/ mean
Z = your mom
Adam's Z-score on a test is +2.50. What does this mean?
Adam's score has a 2.5% chance of being better than any other randomly selected score.
Adam's test score was better than 25% of his peers.
He scored 2.5 standard deviations above the average.
He did terrible.
Joanne's score on a test gives her a Z-score is -1.50. What does this mean?
Joanne didn't take the test yet.
Joanne's test score is 1.50 standard deviations below the average test score.
Joanne did better than 1.50 times her peers.
Joanne's test score, on average, was 1.5 points lower than the other test scores.
What is the Z-score for Tina if she got a 31 on the ACT, the mean was 23 and the SD was 4?
+0.20
+2.00
-2.00
-0.20
What is the Z-score for Paula if she got 1400 on the SAT, the mean was 1100 and the SD was 275?
So if Tina's Z-score is +2.00 and Paula's Z-score is +1.09, who performed better?
Tina's performance is farther above the mean so she did better.
Paula's score is closer to the mean so she did better.
They both did the same.
Kellogg's cereal has an average of 7.6 g of sugar with an SD of 4.5g.
What is the Z-score of Frosted Flakes if it has 11g sugar?
+0.76
-0.74
+0.68
+0.28
What does it mean to have a z-score of z=0 on a quiz?
It means you did better than zero people.
It means you scored the same grade as the average grade.
It means you earned a zero on the quiz.
It means the average score was a zero.
In a factory, the weight of the concrete poured into a mold by a machine follows a normal distribution with a mean of 1150 pounds and a standard deviation of 22 pounds. What weight falls at the 50th percentile?
1106 pounds
1128 pounds
1150 pounds
1172 pounds
Use the image of the normal graph provided. What is the value of the mean?
6
34
52
70
Use the image of the normal graph provided. What is the value of the standard deviation?
6
12
36
18
What percent of scores are below a z-score of z=−1.02 ? (Use your z-table)
15.87%
15.39%
9.68%
84.61%
What percent of scores are above a z-score of z=2.34 ? (Use your z-table)
99.04%
0.96%
98.93%
97.68%
Find the percent. Use the Z-table.
Mean = 30
Standard Deviation = 4
x < 40
99.38%
0.62%
99.40%
.42%
Find the percent. Use the Z-table.
Mean = 30
Standard Deviation = 4
x > 21
98.78%
1.22%
97.56%
2.22%
What is the purpose of z-scores?
to describe the exact location of a score within a distribution
to find the mean of the distribution
to describe the shape of the distribution
to find the standard deviation of the distribution
The sign of the z-score indicates whether the location is above (positive) or below (negative) the mean.
True
False
If you calculated a z-score of -5.37, would that be considered unusual?
Yes
No
Find the z-scores value corresponding if the location is below the mean by 21 a standard deviation.
-0.50
+1.00
+0.50
-1.00
Steve took his math test and scored an 88. If the class average was a 78 with a standard deviation of 5, what percent of students earned a grade that was higher than Steve's grade?
97.72%
42.07%
5%
2.28%
