Question

the two - way table below shows the number of students enrolled in an introductory statistics course at a private university and whether or not their gpa was at or above 3.5 and whether or not they studied 15 or more hours per week.

	studies 15 or more hours per week	studies less than 15 hours per week
students with gpa below 3.5	28	29

what is the approximate probability that an enrolled student holds a gpa of 3.5 or above under the condition that they studied less than 15 hours per week?
\\(\circ\\) a) 47%
\\(\circ\\) b) 60%
\\(\circ\\) c) 67%
\\(\circ\\) d) 70%

Explanation:

Step1: Identify relevant counts

We need the number of students who studied less than 15 hours per week and have GPA 3.5 or above (60) and the total number of students who studied less than 15 hours per week (60 + 29).

Step2: Calculate conditional probability

The formula for conditional probability \( P(A|B)=\frac{P(A\cap B)}{P(B)} \), here \( A \) is "GPA 3.5 or above" and \( B \) is "studied less than 15 hours per week". So we calculate \( \frac{60}{60 + 29} \).
First, find the denominator: \( 60+29 = 89 \).
Then, \( \frac{60}{89}\approx0.674 \), which is approximately 67%.

Answer:

c) 67%