How Probability Distributions Affect Decisions
Imagine if you were offered a job in a different state and a major consideration for you is rent prices (assuming you planned to rent instead of buy). Your main concerns are the affordability in relation to your income and the location/condition of the property. Perhaps you would look for the cheapest rent possible within a quiet, residential community. Or, you might be willing to spend at little more than average to live in the heart of downtown. As you research the city, you learn that the mean for rents of your preferred home size are $1,300 a month. Many people might base their decision on this number alone, but you—equipped with the knowledge of standard deviation—know there is more to that number.
If the most you could afford is $1,100 a month in rent, then a standard deviation of $250 might be good news because the amount you can afford is still within 1 deviation of the mean. With a standard deviation of $75, however, you might be unwilling to make the sacrifices necessary to rent a place that you could afford. Additionally, if you were willing to spend a little more than average to live in a nice place or area, then you could easily find an amazing place with a standard deviation of $100 but might not be able to afford the upgrade with a standard deviation of $300.
In this Discussion, you will use the data that you gathered in the Week 1 Discussion to calculate a standard deviation and explain how this concept can affect decision making.
Locate the data that you gathered for the Week 1 Discussion.
Calculate the sample standard deviation from your cigarette price data in Week 1. Use that (and your sample average and sample size) to calculate the following (assuming a normal distribution):
Within what range would you find 90% of cigarette prices in your area?
What are the chances that someone in your area would pay 4 dollars or less per pack?
What are the chances that someone in your area would pay 10 dollars or less per pack?