Question

Part 1: Use the following steps to create a standard normal in StatKey and answer the following questions about the variable Z.

Go to http://www.lock5stat.com/StatKey/

Click on Normal (This is located in the theoretical distributions section)

Notice in the right hand corner StatKey has a mean of 0 and standard deviation of 1 as default

Notice in the left hand corner are the usual left, right and 2 tail options these will be helpful in the problems below

For each of the following first fill in the plot for the area you are interested in. First find the area using StatKey.   Once you have found the area using StatKey use the standard normal table to also find the area. For each give the area you find on StatKey and the area from the table. Do not round the area   from the table.

1.The area above z= -1.5

2. The area below z=-0.14

3. The area between z=-2.32 and z=2.32

4. Find the endpoint which has 60% of the area below it.

5. Find the endpoint which has 60% of the area above it.

Part 2: For each of the following first fill in the plot for the area you are interested in. Then find the area using StatKey. You will need to change the normal in Statkey to match the mean and standard deviation. Once you have found the area using StatKey use the standard normal table to also find the area. You will need to standardize the value.

For each problem give the area you find on StatKey and the area from the table. Do not round the area from the table.

6. The area above -1.2 on a N(-2,1.5) distribution

7. The area below 0.7 on a N(1,4) distribution

8. The area between -2 and 2 on a N(3.4, 5) distribution

9. Find the endpoint on a N(100,10) distribution which has 74% of the area below it.

10. Find the endpoint on a N(100,10) distribution which has 15% of the area above it.

Part 3: For each of the following follow the steps to find the probability using the standard normal table. As a reminder the steps are listed for you.

How to solve problems involving normal distributions with a Standard Normal Table:

Write out the problem in terms of the original variable.

Draw a picture of the distribution and shade the area of interest under the curve.

Standardize the value (or values) of the original variable

Using the standard normal table find the area to the left of the standardized value. Use this value and the fact that the total area under the curve is equal to 1 to find the value you want.

Write your conclusion in the context of the problem.

11. The average number of acres used for growing tobacco in Kentucky is 75,300 acres per year, with a standard deviation of 5,000 acres. What is the probability that less than 82,315 acres will be used for growing tobacco?

12. The average number of acres used for growing tobacco in Kentucky is 75,300 acres per year, with a standard deviation of 5,000 acres. What is the probability that more than 71,295 acres will be used for growing tobacco

13. The average number of acres used for growing tobacco in Kentucky is 75,300 acres per year, with a standard deviation of 5,000 acres. What is the probability that between 67,250 and 76,250 acres will be used for growing tobacco?

Answer 1

Part 1

1.The area above z= -1.5

From the graph = 0.067
From the ztable = 0.0668

2. The area below z=-0.14

From the graph = 0.444
From the ztable = 0.4443

3. The area between z=-2.32 and z=2.32

Area between (-2.32<x<2.32)= Area below 2.32 - Area below -2.32

From graph = 0.987 - 0.013 = 0.974
From z table = 0.9898
- 0.0102 = 0.9796

4. Find the endpoint which has 60% of the area below it.

From graph = 0.253
from z table = 0.25

5. Find the endpoint which has 60% of the area above it.

From graph = -0.253
from z table = -0.25