POLS210

Assignment 8

Normal Curve

I. Read the instructions 1 a) through d) below and answer the following question:

1. Assume a normal distribution with a mean of 20 and a standard deviation of 5 and find the proportion of the area beyond 30 (i.e. above 30).

a) Draw a normal curve and place the mean and the score 30.

b) Shade the area beyond 30.

c) Translate the score 30 to a z score using the z formula : z=(Xi-Xbar)/s (Remember that Xbar is the mean. Xi is 30 in this quastion.)

d) Find the proportion of the shaded area. (The z table shows the areas outisde of the z scores, so in this question, you just have to read the proportion in the table to find the size of the shaded area.)

 

2. Find the proportion of the area between 30 and the mean.

 

3. Find the proportion of the area below the score of 30.

 

4. Find the proportion of the area below the score of 20. (Remember that the entire area=1. What is the area below 20 then?)

 

5. Find the proportion of the area above the score of 20.

 

II. Assume a normal distribution with a mean of 30 and a standard deviation of 5 and answer the following questions.

 

1. Find the proportion of the area beyond 35 (i.e. above 35).

a) Draw a normal curve and place the mean and the score 35.

b) Shade the area beyond 35.

c) Translate the score 35 to a z score using the z formula.

d) Find the proportion of the shaded area.

 

2. Find the proportion of the area between 35 and the mean.

 

3. Find the proportion of the area below the score of 35.

 

4. Find the proportion of the area below the score of 30.

 

5. Find the proportion of the area above the score of 30.

 

III. Assume a normal distribution with a mean of 120 and a standard deviation of 8, find the proportion of the area beyond 140.

 

IV. Assume a normal distribution with a mean of 80 and a standard deviation of 10, find the proportion of the area beyond 60 (i.e. below 60).

 

V. Assume a normal distribution with a mean of 55 and a standard deviation of 7, find the proportion of the area beyond 40.

 

VI. Assume a normal distribution with a mean of 68 and a standard deviation of 9, find the proportion of the area beyond 75.

 

Obtain an instructor's signature. Take a picture of the assignment and copy and paste it into a Word file. Submit it to Blackboard. (Blackboard allows you to deposit the assignment only once.)