Statistics Standard Deviation Questions

2.

A distribution has a standard deviation of σ = 10. Find the z-score for each of the following locations in the distribution.

a. Above the mean by 5 points.

b. Above the mean by 2 points.

c. Below the mean by 20 points

d. Below the mean by 15 points.

8.

Find the z-score corresponding to a score of X = 45 for each of the following distributions.

a. μ = 40 and σ = 20

b. μ = 40 and σ = 10

c. μ = 40 and σ = 5

d. μ = 40 and σ = 2

16.

A distribution of exam scores has a mean of μ = 78.

a. If your score is X=70, which standard deviation would give you a better grade:

σ = 4 or σ = 8?

b. If your score is X=80, which standard deviation would give you a better grade:

σ = 4 or σ = 8?

Chapter 6. Pages 190-191

8.

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

1. z = -0.25 and z = +0.25
2. z = -0.67 and z = +0.67
3. z =-1.20 and z = +1.20

10.

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

1. 5% in the tail on the left
2. 30% in the tail on the right
3. 65% in the body on the left
4. 80% in the body on the right

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

1. Genius or near genius: IQ over 140
2. Very superior intelligence: IQ from 120-140
3. Average or normal intelligence: IQ from 90-1092.A distribution has a standard deviation of σ = 10. Find the z-score for each of the following locations in the distribution.a. Above the mean by 5 points.b. Above the mean by 2 points.c. Below the mean by 20 pointsd. Below the mean by 15 points.8.Find the z-score corresponding to a score of X = 45 for each of the following distributions.a. μ = 40 and σ = 20b. μ = 40 and σ = 10c. μ = 40 and σ = 5d. μ = 40 and σ = 216. A distribution of exam scores has a mean of μ = 78.a. If your score is X=70, which standard deviation would give you a better grade: σ = 4 or σ = 8?
   b. If your score is X=80, which standard deviation would give you a better grade:
   σ = 4 or σ = 8?
   Chapter 6. Pages 190-1918.What proportion of a normal distribution is located between each of the following z-score boundaries?
   1. z = -0.25 and z = +0.25
   2. z = -0.67 and z = +0.67
   3. z =-1.20 and z = +1.20

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

   1. 5% in the tail on the left
   2. 30% in the tail on the right
   3. 65% in the body on the left
   4. 80% in the body on the right

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

   1. Genius or near genius: IQ over 140
   2. Very superior intelligence: IQ from 120-140
   3. Average or normal intelligence: IQ from 90-109