Discussion of Assignment 6

To answer questions such as those that appear in assignments 6 and 7 it is useful to draw pictures of what is known and not known.

Suppose the property taxes on homes in Gainesville, Florida are approximately normal in distribution, with a mean of $1,400 and a standard deviation of $600. The property tax for one particular home is $1,700.

What proportion of the property taxes exceed $1,700?

Try following these steps:

1. Think about what is known and unknown.
   • Clearly we know the mean and standard deviation and are supposed to assume the population of property taxes is normal. We need to find out what proportion or percent of property taxes are greater than $17,00
2. Draw a picture
   • Example
3. Include what is known and unknown.
   • Example
4. Convert raw score, here $1,700 to a z score in order to use the table of the standard normal distribution
   • z turns out to be .500
   • Example
5. Ask how much of the curve is above this score.
   • Example
6. Refer to the table of the standard normal distribution
7. Find the entry that corresponds to the z score
8. The number is the area under the curve that lies above the z score.
9. In this example the entry is .3085 so 30.85 percent of the area under the normal curve lies above z = .5.
   • Example
10. Draw a conclusion
    • Example
11. You can easily determine how much of the area lies between various points.
    • So you can answer the question above plus others such as what proportion of property taxes are below $1,700?
    • Example

• Any questions? H. T. Reynolds

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