Question

1. According to the empirical rule, in a normally distributed set of data, approximately what percent of the scores will be within 1 standard deviation (-1 to +1) away from the mean?

40%

95%

68%

75%

2. f you took an IQ test and your score was 2 standard deviations above average, assuming normal distribution, approximately what percent of all IQ test takers would your score be higher than?

98%

60%

70%

80%

3. if you took an IQ test and you scored 1 standard deviation below average, assuming normal distribution, approximately what percent of all IQ test takers would your score be higher than?

2.5%

16%

34%

13.5%

4. Which of the following characterization is true about shorter and flatter frequency distribution (relative to normal distribution)?

a. Scores are more spread out, and it will likely have a relatively large standard deviation.

b. It will be negatively skewed.

c. Scores are clustered closely around the mean and will have a relatively small standard deviation.

d. It is called a leptokurtic distribution

Answer 1

(1) Answer: 68%

>> P(-1 < z < 1) = 0.6828 = 68.28% = 68% (Approximately)

(2) Answer: 98%

>> P(z < 2) = 0.9772 = 97.72% = 98% (Approximately)

(3) Answer: 16%

>> P(z < -1) = 0.1587 = 15.87% = 16% (Approximately)

(4) Answer: (a) Scores are more spread out, and it will likely have a relatively large standard deviation.