Jerry has taken a random sample of students and determined the number of electives that each student in his sample took last year. There were 19 students in the sample. Here is the data on the number of electives the 19 students took: 6, 6, 8, 7, 7, 7, 8, 9, 10, 8, 7, 6, 9, 6, 8, 7, 9, 7, 10. The mean of this sample data is 7.63.What is the sample proportion of students who took fewer than the mean number of electives? A. 1019 B. 619 C. 719 D. There is not enough data to answer this question.
Question
Jerry has taken a random sample of students and determined the number of electives that each student in his sample took last year. There were 19 students in the sample. Here is the data on the number of electives the 19 students took: 6, 6, 8, 7, 7, 7, 8, 9, 10, 8, 7, 6, 9, 6, 8, 7, 9, 7, 10. The mean of this sample data is 7.63.What is the sample proportion of students who took fewer than the mean number of electives? A. 1019 B. 619 C. 719 D. There is not enough data to answer this question.
Solution
First, we need to determine how many students took fewer than the mean number of electives. The mean number of electives is 7.63.
Looking at the data, the students who took fewer than the mean are those who took 6 or 7 electives. Counting these, we have: 6, 6, 7, 7, 7, 7, 6, 6, 7, 7. That's 10 students.
The sample proportion is calculated as the number of successes (in this case, students who took fewer than the mean number of electives) divided by the sample size.
So, the sample proportion of students who took fewer than the mean number of electives is 10/19 = 0.5263157894736842.
None of the options A, B, C match this result. Therefore, the correct answer is D. There is not enough data to answer this question.
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