For a population with u=50 and o=8, find the z-score for x=54, x=42, x=62 ,x=48 ,x=52 ,x=34
I shall assume that u (usually typed as mu) is the mean and o (usually typed as sigma) is the standard deviation.
For x = 54, z = (54-50)/8 = +0.5
For x = 34, z = (34-50)/8 = -2
You do the others.
To find the z-score for a given value in a population, you can use the following formula:
z = (x - μ) / σ
where:
- z is the z-score
- x is the given value
- μ is the mean (average) of the population
- σ is the standard deviation of the population
Let's calculate the z-scores for the given values:
1. For x = 54:
z = (54 - 50) / 8
z = 4 / 8
z = 0.5
2. For x = 42:
z = (42 - 50) / 8
z = -8 / 8
z = -1
3. For x = 62:
z = (62 - 50) / 8
z = 12 / 8
z = 1.5
4. For x = 48:
z = (48 - 50) / 8
z = -2 / 8
z = -0.25
5. For x = 52:
z = (52 - 50) / 8
z = 2 / 8
z = 0.25
6. For x = 34:
z = (34 - 50) / 8
z = -16 / 8
z = -2
Therefore, the z-scores for the given values are:
- For x = 54, z = 0.5
- For x = 42, z = -1
- For x = 62, z = 1.5
- For x = 48, z = -0.25
- For x = 52, z = 0.25
- For x = 34, z = -2