A research article reports that the number of group treatment sessions attended by a sample was normally distributed, with a mean of 20 and a standard deviation of 6. Which of the following statements is/are true about the sample?
A) Over 75% attended at least 20 sessions.
B) Over one-third attended more than 26 sessions.
C) Slightly more than 15 % attended less than 14 sessions.
D) Slightly more than 15 % attended less than 8 sessions.

Question

A research article reports that the number of group treatment sessions attended by a sample was normally distributed, with a mean of 20 and a standard deviation of 6. Which of the following statements is/are true about the sample?​
A) ​Over 75% attended at least 20 sessions.
B) ​Over one-third attended more than 26 sessions.
C) ​Slightly more than 15 % attended less than 14 sessions.
D) ​Slightly more than 15 % attended less than 8 sessions.

Quizplus · Accepted Answer

C) is correct because it applies the empirical rule (or 68-95-99.7 rule) for normal distributions. According to this rule, approximately 68% of the data falls within one standard deviation of the mean (20 ± 6), 95% within two standard deviations (20 ± 12), and 99.7% within three standard deviations (20 ± 18). Therefore, slightly more than 15% (100% - 68% / 2) of the sample attended less than 14 sessions (20 - 6 = 14). Choices A, B, and D do not accurately apply the properties of a normal distribution based on the given mean and standard deviation.

A Research Article Reports That the Number of Group Treatment