Question 5 • Probability and Statistics with Applications Honors Sem-2-FL-1210300 (2024-2025)
Students who attend Anytown College pay either in-state or out-of-state tuition, depending on where they reside. The mean and standard deviation of the sum, S, of tuition for a randomly selected pair of in-state and out-of-state students are μS = $6,348.75 and σS = $1,508.48.How can these values be interpreted? Check all that apply.The average of the sums of both types of tuitions would be $6,348.75 for many, many randomly selected pairs of students.Students who pay both types of tuition will pay $6,348.75 per semester.For a pair of randomly selected in- and out-of-state students, the sum of their tuitions is $6,348.75.For a pair of randomly selected in- and out-of-state students, the sum of their tuitions typically varies from the mean of $6,348.75 by about $1,508.48.Students who pay both in- and out-of-state tuition should expect their cost to vary by about $1,508.48 per semester.
Answer
A
The average of the sums of both types of tuitions would be $6,348.75 for many, many randomly selected pairs of students.
B
Students who pay both types of tuition will pay $6,348.75 per semester.
C
For a pair of randomly selected in- and out-of-state students, the sum of their tuitions is $6,348.75.
D
For a pair of randomly selected in- and out-of-state students, the sum of their tuitions typically varies from the mean of $6,348.75 by about $1,508.48.
E
Students who pay both in- and out-of-state tuition should expect their cost to vary by about $1,508.48 per semester.
Explanation
The mean, $6,348.75, describes the average sum of tuition across many randomly selected pairs, so A is correct. The standard deviation, $1,508.48, describes how far a pair’s total typically varies from that mean, so D is correct. The values do not mean that every pair—or an individual student—pays exactly $6,348.75, or that one student pays both tuition amounts.
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