For a distribution
_ _
X = 100 and s=4. If x= X then z=?
If x = 90, then z =?
If z=2, then x=?
If z=1.5, then x =?
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Z = (x - mean)/Standard Deviation
Plug in your values and solve.
To find the value of z in a standard normal distribution, we can use the formula:
z = (x - μ) / σ
Where:
- z is the z-score representing the number of standard deviations from the mean
- x is the value we want to convert to a z-score
- μ is the mean of the distribution
- σ is the standard deviation of the distribution
Given that X = 100 and s = 4, we can substitute these values into the formula to answer the questions:
1. If x = X, then z = ?
z = (X - μ) / σ
z = (100 - μ) / 4
Since we don't have the value of μ (mean) in this question, we can't determine the specific value of z without knowing μ.
2. If x = 90, then z = ?
z = (x - μ) / σ
We need to know the value of μ to calculate the exact z-score for x = 90.
3. If z = 2, then x = ?
Rearranging the formula, we get:
z = (x - μ) / σ
Multiply both sides by σ:
z * σ = x - μ
Add μ to both sides:
x = z * σ + μ
Plug in the known values: z = 2, σ = 4, and μ = 100
x = 2 * 4 + 100
x = 8 + 100
x = 108
Therefore, if z = 2, then x = 108.
4. If z = 1.5, then x = ?
Using the same formula as above:
z = (x - μ) / σ
Rearranging the formula:
x = z * σ + μ
Plug in the known values: z = 1.5, σ = 4, and μ = 100
x = 1.5 * 4 + 100
x = 6 + 100
x = 106
Thus, if z = 1.5, then x = 106.