Deck 4: Normal Distribution and Standard Scores

Question 1

The left tail of a distribution of a continuous variable is pulled extremely to the left. Which of the following would you expect to find given the shape of the distribution?

A) positive skewness statistic
B) negative skewness statistic
C) positive kurtosis statistic
D) negative kurtosis statistic

Answer 1

B

Question 2

A distribution of a continuous variable is extremely peaked. Which of the following would you expect to find given the shape of the distribution?

A) positive skewness statistic
B) negative skewness statistic
C) a positive kurtosis statistic
D) a negative kurtosis statistic

Answer 2

C

Question 3

Which of the following is indicative of a distribution that is positively skewed?

A) A symmetric distribution.
B) A left tail that is substantially pulled to the left.
C) A right tail that is substantially pulled to the right.
D) A very flat distribution.

Answer 3

C

Question 4

Which of the following would be found with a platykurtic distribution?

A) a positive skewness statistic
B) a negative skewness statistic
C) a positive kurtosis statistic
D) a negative kurtosis statistic

Question 5

The range of prices of new condominium sales ranges from $145,000 to $2,376,000. Most of the prices are bunched together in mid to low $200,000. What does this suggest in terms of the shape of the distribution?

A) Negative kurtosis
B) Negative skewness
C) Positive kurtosis
D) Positive skewness

Question 6

Weights (in pounds and ounces) of newborns ranges from 3 pounds 7 ounces to 8 pounds 14 ounces. Most of the weights of newborns bunch together between mid-seven to mid-eight pounds. What does this suggest in terms of the shape of the distribution?

A) Negative kurtosis
B) Negative skewness
C) Positive kurtosis
D) Positive skewness

Question 7

Which of the following is indicative of a distribution that has a skew value of +18.90?

A) A distribution that when split down the middle is an exact mirror image of itself.
B) A left tail that is substantially pulled to the left.
C) A right tail that is substantially pulled to the right.
D) A very peaked distribution.
E) A very flat distribution.

Question 8

Which of the following is indicative of a distribution that has a skew value of -14.76?

A) A distribution that when split down the middle is an exact mirror image of itself.
B) A left tail that is substantially pulled to the left.
C) A right tail that is substantially pulled to the right.
D) A very peaked distribution.
E) A very flat distribution.

Question 9

Which of the following is indicative of a distribution that has a kurtosis value of +7.25?

A) leptokurtic distribution
B) mesokurtic distribution
C) platykurtic distribution
D) positive skewness
E) negative skewness

Question 10

Which of the following is indicative of a distribution that has a kurtosis value of -11.56?

A) leptokurtic distribution
B) mesokurtic distribution
C) platykurtic distribution
D) positive skewness
E) negative skewness

Question 11

The population mean of a distribution that is approximately normal is 500 and the population standard deviation is 100. What is the mean of the standardized distribution for this variable?

A) 0
B) 10
C) 100
D) 500
E) Cannot be determined from this information

Question 12

The population mean of a distribution that is approximately normal is 72 and the population standard deviation is 9. What is the mean of the standardized distribution for this variable?

A) 0
B) 3
C) 9
D) 72
E) Cannot be determined from this information

Question 13

A distribution has a mean of $25,000 and a standard deviation of $5,000. Which of the following is correct based on applying the Empirical Rule?

A) About 68% of the distribution is between $20,000 and $30,000.
B) About 95% of the distribution is between $20,000 and $30,000.
C) About 95% of the distibution is between $15,000 and $40,000.
D) All of the values fall between $10,000 and $40,000.

Question 14

Apply the Empirical Rule to a distribution that has a mean of 275 and a standard deviation of 36. Which one of the following is correct?

A) About 34% of the distribution is between 239 and 311.
B) About 68% of the distribution is between 275 and 311.
C) About 95% of the distribution is between 203 and 347.
D) All of the distribution is between 167 and 383.

Question 15

Applying the Empirical Rule to a distribution with a mean of 80 and standard deviation of 5, which one of the following is correct?

A) About 34% of the values are located between 80 and 90.
B) About 95% of the values are between 70 and 90.
C) About 75% of the values are between 75 and 85.
D) All values fall between 65 and 95.

Question 16

Which one of the following is a correct statement based on a distribution with a mean of 750 and standard deviation of 25?

A) About 2.5% of the scores in the distribution are greater than 675.
B) About 50% of the scores in the distribution are less than 725.
C) About 84% of the scores in the distribution are less than 775.
D) About 95% of the scores in the distribution are less than 700.

Question 17

A distribution of 400 scores is approximately normally distributed. The mean of the distribution is 50 and the standard deviation is 10. What percentage of scores are less than a value of 30?

A) about 2.5%
B) about 16%
C) about 34%
D) about 50%

Question 18

A distribution is approximately normal with a population mean of 80 and population standard deviation of 9. Approximately what percentage of scores fall between 71 and 89?

A) About 1/3
B) About 2/3
C) About 95%
D) About 99%

Question 19

What is the percentile rank of the score 610 in a unit normal distribution that has a population mean of 500 and standard deviation of 100?

A) Approximately 1
B) Approximately 87
C) Approximately 100
D) Approximately 110

Question 20

What is the 80th percentile of a distribution that is approximately normally distributed with a population mean of 75 and variance of 16?

A) Approximately 72%
B) Approximately 78%
C) Approximately 84%
D) Approximately 95%

Question 21

A standardized score of 2.22 is interpreted as which one of the following?

A) Approximately 2.25% of the distribution is right of the mean.
B) The mean is 2.22.
C) The score is approximately 2 and 1/4 standard deviation units to the right of the mean.
D) The standard deviation is 2.22.

Question 22

After completion of a training program, scores on the satisfaction survey are standardized. The following reflect the standardized results for each component of the satisfaction survey: a) satisfaction with the physical environment, .86; b) satisfaction with the material presented, 2.70; c) satisfaction with the handouts, 1.37; and d) satisfaction with the facilitator, 3.25. Which aspect of satisfaction is farthest from the average?

A) satisfaction with the physical environment
B) satisfaction with the material presented
C) satisfaction with the handouts
D) satisfaction with the facilitator

Question 23

A new instructor receives the following standardized scores based on their first teaching evaluation: a) concern for students, -1.25; b) organization of the course, .35; c) facilitation of learning, .12; d) classroom materials, -2.10. In which area did the instructor score farthest from the average?

A) concern for students
B) organization of the course
C) facilitation of learning
D) classroom materials

Question 24

Which of the following represents the interpretation of a standardized score of -1.5?

A) One and one-half percent (1.5%) of the scores are left of the mean.
B) One and one-half percent (1.5%) of the scores are right of the mean.
C) The score is 1.5 standard deviation units from the mean.
D) The standard deviation of the variable is 1.5.

Question 25

An auditor for the national accrediting agency for the college provides the administration with standardized scores for the areas they were assessed. The standardized scores include: a) recruitment, -1.50; b) assessment, +1.25; c) faculty qualifications, +.75; and d) program offerings, -1.00. In which area did the college score closest to the average?

A) recruitment
B) assessment
C) faculty qualifications
D) program offerings

Question 26

What is the proportion of the area below z = +.86 assuming a normal distribution and referring to the table for N(0,1)?

Question 27

What is the proportion of the area below z = -.22 assuming a normal distribution and referring to the table for N(0,1)?

Question 28

What is the proportion of the area below z = +1.10 assuming a normal distribution and referring to the table for N(0,1)?

Question 29

What is the percentile rank of the score 95 in N(90,100)?

Question 30

What is the 40th percentile of N(36,36)?