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WorksheetsZ Score word problems
Total questions: 15
Worksheet time: 2hrs 7mins
Name
Class
Date
1.
What is the purpose of z-scores?
a)
to describe the exact location of a score within a distribution
b)
to find the mean of the distribution
c)
to describe the shape of the distribution
d)
to find the standard deviation of the distribution
2.
What is the formula to find the z-score for population?
a)
z=X-M
b)
z=σ-M/μ
c)
z/M=μ
d)
z=X-μ/σ
3.
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?
a)
-5
b)
-2
c)
2
d)
5
4.
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. Approximately 95% of molds filled by this machine will hold weights in what interval?
a)
1084 to 1216 pounds
b)
1106 to 1150 pounds
c)
1106 to 1194 pounds
d)
1128 to 1172 pounds
5.
A national achievement test is administered annually to 3rd graders. The test has a mean score of 100 and a standard deviation of 15. If Jane's z-score is 1.20, what was her score on the test?
a)
82
b)
88
c)
100
d)
118
6.
The average waist size for teenage males is 29 inches with a standard deviation of 2 inches.
If waist sizes are normally distributed, determine the z-score of a teenage male with a 33 inch waist.
If waist sizes are normally distributed, determine the z-score of a teenage male with a 33 inch waist.
a)
2
b)
1
c)
-2
d)
-1
7.
The shelf life of a particular dairy product is normally distributed with a mean of 12 days and a standard deviation of 3 days.
About what percent of the products last between 12 and 15 days?
About what percent of the products last between 12 and 15 days?
a)
68%
b)
34%
c)
16%
d)
2.5%
8.
The Floppy Disk Company makes 3.5 inch floppy disks for disk drives that are 3.7 inches wide. The size of a manufactures disk is normally distributed with a standard deviation of 0.1 inches. The company manufactures 1000 disks every hour.
In one hour, how many disks would you expect to be between 3.4 inches and 3.7 inches?
In one hour, how many disks would you expect to be between 3.4 inches and 3.7 inches?
a)
819 disks
b)
23 disks
c)
500 disks
d)
0 disks
9.
Women’s heights have a mean of 63.6 in. and a standard deviation of 2.5 inches. The z score corresponding to a woman with a height is 2.56. How tall is the woman?
a)
24.42 in
b)
70 in
c)
28in
d)
68.6in
10.
Standard deviation tells us how spread out a symmetric distribution is.
Since a Z-score tells us how many standard deviations away from average something is, what does a high Z-score mean?
Since a Z-score tells us how many standard deviations away from average something is, what does a high Z-score mean?
a)
It's way higher than average
b)
tl:dr
c)
you're in trouble?
d)
you need a doctor
11.
Adam's Z-score on a test is +2.5. What does this mean?
a)
He'd better start studying.
b)
He did better than EVERYONE.
c)
He scored 2.5 standard deviations above the average.
d)
He did terrible.
12.
Joanne's Z-score is -1.5. What does this mean?
a)
She didn't take the test yet.
b)
She scored 1.5 standard deviations below the average.
c)
She did better than most people.
d)
No clue
13.
Z-scores are calculated by subtracting the mean from the score and then dividing by the standard deviation. Which of the following is a formula that describes this calculation?
a)
Z = (score - mean) / stand. devation
b)
Z = (mean - score) / stand. dev.
c)
Z = score/stand. dev/ mean
d)
Z = dragonball
14.
If Gonzalo's score is 87, the class average is 82, and the SD is 4, what is Gonzalo's Z-score?
a)
-1.25
b)
+1.25
c)
+1.20
d)
+1.02
15.
What is the Z-score for Paula if she got 1400 on the SAT, the mean was 1100 and the SD was 275?
a)
-1.90
b)
-1.09
c)
+1.09
d)
+1.90
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