A car wash owner wants to know the average time customers take to wash their cars. This information can help them improve their efficiency and provide better service.
Random Variables:
* \(X_i\): The time taken by the \(i-th\) customer to wash their car.
* \(n\): The total number of customers.
Probability Distribution:
We assume that the time taken by each customer to wash their car is independent and identically distributed (i.i.d.). This means that the probability distribution of \(X_i\) is the same for all customers.
Expected Value:
The expected value of the time taken by a customer to wash their car is given by:
$$E(X) = \frac{1}{n}\sum_{i=1}^n X_i$$
Data Collection:
The car wash owner can collect data on the time taken by customers to wash their cars by using a stopwatch or by installing sensors in the car wash.
Analysis:
Once the data has been collected, the car wash owner can calculate the expected value of the time taken by a customer to wash their car. This information can then be used to improve the efficiency of the car wash and provide better service to customers.
Conclusion:
By calculating the expected value of the time taken by a customer to wash their car, the car wash owner can gain valuable insights into the operation of their business. This information can help them make informed decisions about how to improve their efficiency and provide better service to customers.
