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.
if a customer prefers in - person banking, what is the conditional relative frequency that they primarily use a savings account?

Explanation:

Step1: Recall the formula for conditional relative frequency

Conditional relative frequency \(=\frac{\text{Frequency of the joint event}}{\text{Frequency of the condition}}\). Here, the condition is "in - person banking" (\(n = 300\)), and the joint event is "in - person banking and savings account".

Step2: Identify the frequencies from the table

The number of customers who prefer in - person banking is \(n(\text{in - person})=300\). The number of customers who prefer in - person banking and primarily use a savings account is \(n(\text{in - person and savings}) = 150\).

Step3: Calculate the conditional relative frequency

Using the formula \(f=\frac{n(\text{in - person and savings})}{n(\text{in - person})}\), substitute \(n(\text{in - person and savings}) = 150\) and \(n(\text{in - person})=300\). So, \(f=\frac{150}{300}=0.5\)

Answer:

\(0.5\)