Question

a. Describe a Normal Distribution of a variable.

b. Where in nature can you find a Normal Distribution?

c. What are the characteristics of a Normal Distribution?

d. What are the parameters of a Normal Distribution?

d. What information can you determine from a normal distribution?

In each of the following Exercises 6.4-6.11, assume that the variable under consideration has a density curve. Note that the answers required here may be only approximately correct.

6.4 The percentage of all possible observations of the variable that lie between 7 and 12 equals the area under its density curve between _______ and _______, expressed as a percentage.

6.5 The percentage of all possible observations of the variable that lie to the right of 4 equals the area under its density curve to the right of _______, expressed as a percentage.

6.6 The area under the density curve that lies to the left of 10 is 0.654. What percentage of all possible observations of the variable are

• a.  less than 10?
• b.  at least 10?

6.7 The area under the density curve that lies to the right of 15 is 0.324. What percentage of all possible observations of the variable

• a.  exceed 15?
• b.  are at most 15?

6.8 The area under the density curve that lies between 30 and 40 is 0.832. What percentage of all possible observations of the variable are either less than 30 or greater than 40?

6.9 The area under the density curve that lies between 15 and 20 is 0.414. What percentage of all possible observations of the variable are either less than 15 or greater than 20?

6.10 Given that 33.6% of all possible observations of the variable exceed 8, determine the area under the density curve that lies to the

• a.  right of 8.
• b. left of 8.

6.11 Given that 28.4% of all possible observations of the variable are less than 11, determine the area under the density curve that lies to the

• a. left of 11.
• b.  right of 11.

Answer 1

As area of the total normal distribution curve is 1

6.4 There is no sufficient information about distribution, one needs standard deviation and mean to get the answer

6.5 Here also information arr not sufficient to dolso

6.6 i t the left the area will be as stated is 0.654

Ii to the right of 10 or at least 10 is 1-0.654=0.346

6.7a exceed 15 is means right to 15 is 0.324

B at most 15 means left to point 15 is .676

6.8 in between 30 and 40 is 0.832 then less than 30 and more than 40 is 1-0.832 =0.168

6.9 the area under curve less than 15 and more than 20 is =1-0.414 = 0.586

6.10 Exceeding 8 is 0.336 and less than 8 is 1-.336=.664

6.11less than 11 is means left of ,11 is 0.284 and right of them is 1-0.284=.716