Question

For the study described​ below, identify the population parameter.

A bank manager wants to know the average amount of time customers of his bank have to wait in line. 300 customers were polled and asked their average wait time at the bank. 27 of the 300 people were extremely dissatisfied with the amount of time they had had to wait in line in recent months.

Answer 1

The population parameter in the bank manager's study is the average wait time for all customers at the bank. Various examples illustrate how mean, standard deviation, and variance are measured and used to understand waiting times across different services.

Step-by-step explanation:

The population parameter of interest for the bank manager's study is the average wait time for all customers of the bank. This is often denoted by the Greek letter mu (μ), which represents the mean of the entire population. The bank manager wants to estimate this parameter using the sample data collected from 300 customers.

In the examples provided:

• The post office found that with individual lines, the standard deviation of waiting times was 7.2 minutes, and with a single main line, the standard deviation for a sample of 25 customers was 3.5 minutes, suggesting a potentially lower variability in waiting times with a single line system.
• Supermarket A and B both have an average wait time of five minutes, but Supermarket A has a lower standard deviation of two minutes, compared to four minutes for Supermarket B, indicating that wait times are more consistent at Supermarket A.
• For the store modeled with an exponential distribution, an average waiting time between customer arrivals is calculated to be two minutes, and it takes six minutes on average for three customers to arrive when the store opens.
• A random sample of 30 patients in a doctor's office had a standard deviation of 4.1 minutes, which was higher than the previously thought variability, thus prompting the doctor to believe the variance of waiting times might be greater than originally estimated.
• In an example of emergency room wait times, a hospital survey of 70 patients resulted in a sample mean of 1.5 hours and a sample standard deviation of 0.5 hours.
• The waiting time for a rural bus was uniformly distributed between 0 to 75 minutes according to a survey of 100 riders.

Overall, these examples demonstrate the concepts of mean, standard deviation, and variance in the context of waiting times for different services, with an emphasis on understanding and potentially improving customer experience.