A distribution has a standard deviation of _ _ 12. Find the z-score for each of the following locations in the distribution.
a. Above the mean by 3 points.
b. Above the mean by 12 points.
c. Below the mean by 24 points.
d. Below the mean by 18 points.
Z = (score-mean)/SD
a. (score-mean) = 3
Z = 3/12 = ?
Use similar process for the remaining problems.
To find the z-score for a given location in a distribution, you need to use the formula:
z = (x - μ) / σ
Where:
- z is the z-score
- x is the value in the distribution
- μ is the mean of the distribution
- σ is the standard deviation of the distribution
In this case, the standard deviation is given as 12 for the distribution. To find the z-scores for the given locations, we need to know the mean of the distribution as well. Once we have the mean, we can plug the values into the formula to find the z-scores.
Let's go through each part of the question:
a. Above the mean by 3 points:
To find the z-score, we need to know the mean of the distribution. Let's say the mean is μ. So, we can calculate the z-score as:
z = (μ + 3 - μ) / 12
= 3 / 12
= 0.25
b. Above the mean by 12 points:
Using the same formula:
z = (μ + 12 - μ) / 12
= 12 / 12
= 1
c. Below the mean by 24 points:
z = (μ - 24 - μ) / 12
= -24 / 12
= -2
d. Below the mean by 18 points:
z = (μ - 18 - μ) / 12
= -18 / 12
= -1.5
So, the z-scores for the given locations are:
a. 0.25
b. 1
c. -2
d. -1.5