Question

total students surveyed: 300
less than $20:
save: 60 students
spend: 40 students
$20 to $50:
save: 80 students
spend: 70 students
more than $50:
save: 30 students
spend: 20 students

given a student spends their allowance, what is the conditional relative frequency that their allowance is more than $50?

Explanation:

Step1: Recall the formula for conditional relative frequency

The formula for conditional relative frequency is \(P(A|B)=\frac{n(A\cap B)}{n(B)}\). Here, event \(A\) is "allowance is more than $50" and event \(B\) is "spends their allowance".

Step2: Identify the values from the table

From the table, the number of students who spend their allowance (\(n(B)\)) is \(130\), and the number of students who spend their allowance and have an allowance more than $50 (\(n(A\cap B)\)) is \(20\).

Step3: Calculate the conditional relative frequency

Substitute the values into the formula: \(P=\frac{20}{130}=\frac{2}{13}\approx0.15\)

Answer:

\(0.15\)