A bank with a branch located in a commercial district of a city has the business objective of developing an improved process for serving customers during the noon-to-1pm lunch period. Management decides to first study the waiting time in the current process. The waiting time is defined as the number of minutes that elapse from when the customer enters the queue until he/she reaches the teller’s window. In addition, suppose that another branch, located in a residential area, is also concerned with improving the process of serving customers in the noon-to-1 pm lunch period and data were collected at random at these branches and recorded below; No of Customers Commercial dist branch (time) Residential area branch (time) 1 – 5 3 3 6 - 10 5 6 11 - 15 8 5 16 – 20 8 3 21 - 25 4 2 Required Which of the branches has a relatively better mean waiting time? Which shop can be surer of meeting the mean waiting time at the two branches? Assuming that the population variances from both banks are unequal, is there evidence of a difference in the mean waiting time between the two branches at 5% significant level?
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
A bank with a branch located in a commercial district of a city has the business objective of developing an improved process for serving customers during the noon-to-1pm lunch period. Management decides to first study the waiting time in the current process. The waiting time is defined as the number of minutes that elapse from when the customer enters the queue until he/she reaches the teller’s window. In addition, suppose that another branch, located in a residential area, is also concerned with improving the process of serving customers in the noon-to-1 pm lunch period and data were collected at random at these branches and recorded below;
|
No of Customers |
Commercial dist branch (time) |
Residential area branch (time) |
|
1 – 5 |
3 |
3 |
|
6 - 10 |
5 |
6 |
|
11 - 15 |
8 |
5 |
|
16 – 20 |
8 |
3 |
|
21 - 25 |
4 |
2 |
Required
- Which of the branches has a relatively better mean waiting time?
- Which shop can be surer of meeting the mean waiting time at the two branches?
- Assuming that the population variances from both banks are unequal, is there evidence of a difference in the mean waiting time between the two branches at 5% significant level?
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