Question

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

1. Above the mean by 15 points.

Answer: ______________

2. Above the mean by 25 points.

Answer: _________________

3. Below the mean by 20 points.

Answer: ___

4. Below the mean by 5 points.

Answer: _________

2. For a distribution with a standard deviation of σ = 12, describe the location of each of the following z-scores in terms of its position relative to the mean. For example, = +1.00 is a location that is 12 points above the mean.

1. z = +2.00         Answer:____________

2. z = +.50           Answer: ____________

3. z = -1.00          Answer:____________

4. z = -0.25          Answer:_____________

Answer 1

Q.1) A distribution has a standard deviation of σ = 10

We want to find, the z-scores for the following cases,

a) Above the mean by 15 points.

z-score = 15/10 = 1.5

=> z = +1.5

b) Above the mean by 25 points.

z-score = 25/10 = 2.5

=> z = +2.5

c) Below the mean by 20 points

z-score = -20/10 = -2.0

=> z = -2.0

d) Below the mean by 5 points

z-score = -5/10 = -0.5

=> z = -0.5

Q.2) For a distribution with a standard deviation of σ = 12

a) 2.00 * 12 = 24

Therefore, z = +2.00 is a location that is 24 points above the mean.

b) 0.50 * 12 = 6

Therefore, z = +0.50 is a location that is 6 points above the mean.

c) -1.00 * 12 = -12

Therefore, z = -1.00 is a location that is 12 points below the mean.

a) -0.25 * 12 = -3

Therefore, z = -0.25 is a location that is 3 points below the mean.