# Normal Distribution, Standard Deviation, and Z-Score

1. What is sampling with replacement and why is it used?

2. What proportion of a normal distribution is located between each of the following z-score boundaries?

a. z=-0.50 and z=+0.50

b. z=-0.90 and z=+0.90

c. z=-1.50 and z=+1.50

3. Find the z-score location of a vertical line that separates a normal distribution as described in each of the following.

a. 20% in the tail on the left

b. 40% in the tail on the right

c. 75% in the body on the left

d. 99% in the body on the right

4. For a normal distribution with a mean of µ=80 and a standard deviation of σ=20, find the proportion of the population corresponding to each of the following?

a. scores greater than 85

b. scores less than 100

c. scores between 70 and 90

5. IQ test scores are standardized to produce a normal distribution with a mean of µ=100 & a standard deviation of σ=15. Find the proportion of the population for each of the following IQ categories.

a. Genius or near genius: IQ over 140

b. Very superior intelligence: IQ from `120 to 140

c. Average or normal intelligence: IQ from 90 to 100

6. Information from the Department of Motor Vehicles indicates that the average age of licensed drivers is µ=39.7 years with a standard deviation of σ=12.5 years. Assuming that the distribution of drivers age is approximately normal,

a. What proportion of licensed drivers are more than 50 years old?

b. What proportion of licensed drivers are less than 30 years old?

#### Solution Preview

ans:

1. After we pick a sample from the whole population and then return that sample back to the whole population, we call this procedure a sample with replacement. Why we use this? Because in some cases, we need the population size remain the same at all times.

2. From z table

a. ...

#### Solution Summary

The solution gives detailed steps on answerting 6 questions regarding on probability calculation assuming the normal distribution. All formula and calcuations are shown and explained.