WorksheetsNormal Distribution and Z Scores
Total questions: 20
Worksheet time: 20mins
The value of the mean and standard deviation of a standard normal distribution is __ and __ respectively.
0 and 1
μ and σ
1 and 0
σ and μ
The wider the width of the normal curve, the
higher its peak
larger its sd
lower its peak
smaller its sd
What is the area for the left side of the curve from the mean?
1
0.75
0.5
0.25
How many standard scores is 14 located if a set of scores is normally distributed with a mean of 12 and a standard deviation of 0.5?
2 standard scores to the left
2 standard scores to the right
4 standard scores to the left
4 standard scores to theright
In a normal distribution, the z-score for the mean is 0.
True
False
The weight of adult male grizzly bears living in the wild in the continental United States is approximately normally distributed with a mean of 500 pounds and a standard deviation of 50 pounds. The weight of adult female grizzly bears is approximately normally distributed with a mean of 300 pounds and a standard deviation of 40 pounds. Approximately, what would be the weight of a female grizzly bear with the same standardized score (z-score) as a male grizzly bear with a weight of 530 pounds?
276 pounds
324 pounds
330 pounds
340 pounds
530 pounds
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.
2
1
-2
-1
The scores on a university examination are Normally distributed with a mean of 62 and a standard deviation of 11. If the bottom 5% of students will fail the course, what is the lowest mark that a student can have and still be awarded a passing grade?
40
43
44
57
62
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?
.9772
.93
.05
.0228
The heights of students in a class follow a normal distribution with a mean of 65 inches and a standard deviation of 3 inches. John is 70 inches tall, while Sarah is 67 inches tall. Calculate the z-scores for John and Sarah and determine who is taller than their peers.
John is relatively taller than Sarah.
Sarah is relatively taller than John.
John and Sarah are equally tall.
insufficient information to determine who is relatively taller.
The average waist size for teenage males is 29 inches with a standard deviation of 1.4 inch. If waist sizes are normally distributed, estimate the proportion of teenagers who will have waist sizes greater than 31 inches?
92.4%
10.5%
16%
7.6%
The weights of laboratory cockroaches follow a Normal distribution with mean 80 grams and standard deviation 2 grams. The following figure is the Normal curve for this distribution of weights.
Point C on this Normal curve corresponds to
84 grams.
82 grams.
78 grams.
76 grams.
74 grams.
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?
1084 to 1216 pounds
1106 to 1150 pounds
1106 to 1194 pounds
1128 to 1172 pounds
On a standardized exam, the scores are normally distributed with a mean of 75 and a standard deviation of 10. Find the z-score of a person who scored 45 on the exam.
-3
3
1.44
2
On a standardized exam, the scores are normally distributed with a mean of 500 and a standard deviation of 25. Find the z-score of a person who scored 525 on the exam.
1
-1
0
2
On a standardized exam, the scores are normally distributed with a mean of 51 and a standard deviation of 10. Find the z-score of a person who scored 27 on the exam.
-2.4
2.4
1.51
-1.51
On a standardized exam, the scores are normally distributed with a mean of 400 and a standard deviation of 40. Find the z-score of a person who scored 472 on the exam.
1.8
-1.8
0.76
-0.76
On a standardized exam, the scores are normally distributed with a mean of 300 and a standard deviation of 20. Find the z-score of a person who scored 294 on the exam.
-0.3
0.5
0.3
0.95
On a standardized exam, the scores are normally distributed with a mean of 300 and a standard deviation of 40. Find the z-score of a person who scored 400 on the exam.
2.5
25
2.5%
-2.5
On a standardized exam, the scores are normally distributed with a mean of 750 and a standard deviation of 100. Find the z-score of a person who scored 580 on the exam.
-1.7
1.7%
1.12
1.7
