Assignment 10

Normal Curve

 

I. Assume a normal distribution with a mean of 20 and a standard deviation of 5 and answer the following questions.

 

1. 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.

d) Find the proportion 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.

 

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

 

II. Given a normal distribution with a mean of 75 and a standard deviation of 20, find the z score for the following scores.

a) 80

b) 40

 

III. Consider the following z scores. Use the standard normal table (i.e. z table) and provide the appropriate proportion.

a) Find the area between the mean and a z score of 1.3.

b) Find the area beyond a z score of 2.96

c) Find the area below a z score of 1.55

 

IV. Assume a normal distribution with a mean of 30 and a standard deviation of 8.

a) Find the proportion of area between the mean and a score of 15.

b) Find the proportion of the area above a score of 11.

c) Find the proportion of the area between 20 and 35.

 

V. Consider the exam results that approximate a normal curve with a mean of 70 and a standard deviation of 15. You got a 75 on the exam and your friend got a 80. Find the proportion of students between your score and your friendís score.