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Normal Distribution and Z Score

Total questions: 20

Worksheet time: 20mins

Name
Class
Date
1.

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.

a)

-3

b)

3

c)

1.44

d)

2

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.

a)

1

b)

-1

c)

0

d)

2

3.

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.

a)

-2.4

b)

2.4

c)

1.51

d)

-1.51

4.

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.

a)

1.8

b)

-1.8

c)

0.76

d)

-0.76

5.

In a normal distribution, the z-score for the mean is 0.

a)

True

b)

False

6.

The # of standard deviations an observation falls from the center of a Normal distribution.

a)

Z-score

b)

t-score

c)

Standard Error

d)

Percentile

7.

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.

a)

John is relatively taller than Sarah.

b)

Sarah is relatively taller than John.

c)

John and Sarah are equally tall.

d)

insufficient information to determine who is relatively taller.

8.

In this formula, the y is one of the cut points in a Normal curve.

a)

True

b)

False

9.

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

10.

In a normal distribution, what does a z-score of 0 represent?

a)

Mode

b)

Median

c)

Standard Deviation

d)

Mean

11.

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?

a)

276 pounds

b)

324 pounds

c)

330 pounds

d)

340 pounds

e)

530 pounds

12.

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.  

a)

2

b)

1

c)

-2

d)

-1

13.

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?

a)

.9772

b)

.93

c)

.05

d)

.0228

14.

The z-score represents.....

a)

the amount of standard deviations a data value is above or below the mean.

b)

the percentile the data value is above or below the mean.

c)

the amount of standard deviations a data value is above or below the median.

d)

the percent the data value is above or below the mean.

15.

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?

a)

40

b)

43

c)

44

d)

57

e)

62

16.

The z-score represents....

a)

the amount of standard deviations a data value is above or below the mean.

b)

the amount of standard deviations a data value is above or below the media .

c)

the percentile the data value is above or below the mean.

d)

the percent the data value is above or below the mean.

17.

So, y values represent the actual, measurements that we are interested in.

a)

True

b)

False

18.

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

a)

84 grams.

b)

82 grams.

c)

78 grams.

d)

76 grams.

e)

74 grams.

19.

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?

a)

92.4%

b)

10.5%

c)

16%

d)

7.6%

20.

Which one is CORRECT?

a)

the bigger the Z-score, the data is closed to the mean

b)

the bigger the Z-score, then the more extreme the data will be

c)

the bigger the Z-score, the more usual is the data