Question

a regional bank is analyzing its customer base to improve its services and offerings.
the bank categorizes its customers based on their preferred banking method (online vs. in person) and their primary account type (checking vs. savings). here is the collected data for a sample of 600 customers:

• 300 customers prefer online banking, with 180 primarily using a checking account.
• the total number of customers who prefer in - person banking and primarily use a savings account is 150.

the bank is interested in understanding the distribution and preferences of its customers to tailor its marketing strategies more effectively.
120 online banking customers use a savings account. what is the conditional relative frequency of online banking customers who primarily use a savings account?

Explanation:

Step1: Recall the formula for conditional relative frequency

Conditional relative frequency \(=\frac{\text{Number of favorable cases}}{\text{Total number of cases in the condition}}\)
Here, the condition is "online banking customers", and the favorable cases are "online - banking customers who use a savings account"
The number of online - banking customers \(= 300\) (from the total of the "Online" column). The number of online - banking customers who use a savings account \(=150\) (from the "Online" row and "Savings Account" column)

Step2: Calculate the conditional relative frequency

Using the formula \(=\frac{150}{300}\)
Simplify the fraction \(\frac{150}{300}=\frac{1}{2}=0.5\) (Wait, there is a mistake. Let's re - check.
The correct formula for conditional relative frequency: If we want to find the conditional relative frequency of online banking customers who use a savings account.
The formula for conditional probability \(P(A|B)=\frac{n(A\cap B)}{n(B)}\)
Let \(A\) be the event of using a savings account and \(B\) be the event of online banking.
\(n(A\cap B) = 150\) (number of online - banking customers with savings accounts), \(n(B)=300\) (total number of online - banking customers)
\(P(A|B)=\frac{150}{300}=0.5\) (No, wait the problem says "120 online banking customers use a savings account". Wait, no, looking at the table:
The number of online - banking customers (total of the "Online" column) is \(180 + 120=300\). The number of online - banking customers who use a savings account is \(150\) (from the "Online" row and "Savings Account" cell).
Wait, no, another way:
The conditional relative frequency of \(A\) (use savings account) given \(B\) (online banking) is \(\frac{\text{Number of online - banking customers with savings accounts}}{\text{Total number of online - banking customers}}\)
From the table:
Total online - banking customers \(=180 + 120=300\) (checking + savings in online)
Number of online - banking customers with savings accounts \(=150\) (from the savings row and online column)
\(=\frac{150}{300}=0.5\) (No, wait, the problem statement says "120 online banking customers use a savings account"? No, looking at the table:
In the "Online" column: "Checking Account" has \(180\), "Savings Account" has \(120\). So total online banking customers \(180 + 120=300\). The number of online banking customers who use a savings account is \(120\)
So conditional relative frequency \(=\frac{120}{300}\)

Step3: Simplify the fraction

\(\frac{120}{300}=\frac{120\div60}{300\div60}=\frac{2}{5}=0.4\)

Answer:

\(0.4\)