Question

3.27. All the workers at a certain company drive to work and park in the company's lot. The company is interested in estimating the average number of workers in a car. Which of the following methods will enable the company to estimate this quantity? Explain your answer.

1. Randomly choose n workers, find out how many were in the cars in which they were driven, and take the average of the n values.

2. Randomly choose n cars in the lot, find out how many were driven in those cars, and take the average of the n values.

Short answer

However, in the second case, we choose n cars (there is no chance of repeating the number of passengers in a car in this case), which gives us the average of n different values. As a result, this is a more accurate method of estimating the average number of passengers travelling in a car.

Step-by-step solution

Step1:the average number of workers in a car.(case1)

In the first option, we pick n workers and count the number of people in the cars they drive. As a result, there is a chance that some people will travel in the same car, and we will end up counting the same car more than once.

2Step2:the average number of workers in a car.(case2) 

However, in the second case, we choose n cars (there is no chance of repeating the number of passengers in a car in this case), which gives us the average of n different values. As a result, this is a more accurate method of estimating the average number of passengers travelling in a car.

the average number of workers in a car. (case 3)

$3$We can say in terms of probability that the probability of events is simply the sum of the probabilities of individual events when they are independent. Choosing cars is independent because the number of passengers in each car is independent, but choosing people is not independent because the number of passengers in the cars travelled by them may be dependent if they travel in the same car.