Question

A company compiles data on a variety of issues in education. In 1998 the company reported that the national college freshman-to-sophomore retention rate was 77%. Consider colleges with freshman classes of 300 students. Use the 68-95-99.7 rule to describe the sampling distribution model for the percentage of students expected to return for their sophomore years. Do you think the appropriate conditions are met? Are the conditions necessary to use a normal model met?

A. Yes, all the conditions are met.
B. No, the success/failure condition is not met.
C. No, the randomization and success/failure conditions are not met.
D. No, the randomization and 10% conditions are not met.
E. No, the 10% and success/failure conditions are not met.
F. No, the randomization condition is not met.
G. No, the 10% condition is not met.
H. No, none of the conditions are met.

Answer 1

The sampling distribution model for the percentage of students expected to return for their sophomore years can be described using the 68-95-99.7 rule. However, the appropriate conditions to use a normal model are not met.

Step-by-step explanation:

The sampling distribution model for the percentage of students expected to return for their sophomore years can be described using the 68-95-99.7 rule, also known as the empirical rule. According to this rule, approximately 68% of the colleges will have a freshman-to-sophomore retention rate between 68% and 86%, approximately 95% of the colleges will have a retention rate between 59% and 95%, and approximately 99.7% of the colleges will have a retention rate between 50% and 104%. These intervals are based on the assumption that the distribution of the retention rates follows a normal distribution.

To determine if the appropriate conditions are met to use a normal model, we need to consider the randomization and success/failure conditions. Since the data is based on a national college freshman-to-sophomore retention rate, we can assume that the data was collected randomly. However, without further information about the data collection process, we cannot be certain. As for the success/failure condition, we don't have information on the number of colleges with freshman classes of 300 students, so we cannot determine if this condition is met. Therefore, the answer is C. No, the randomization and success/failure conditions are not met.