A normal distribution has mean of 7 and standard deviation of 4. What is the raw score of X corresponding to z= -1.25?
Z = (score-mean)/SD
-1.25 = (x-7)/4
Solve for x.
To find the raw score corresponding to a given z-score in a normal distribution, we use the formula:
x = mean + (z * standard deviation)
In this case, the given z-score is -1.25, the mean is 7, and the standard deviation is 4.
Substituting these values into the formula, we get:
x = 7 + (-1.25 * 4)
Calculating this, we have:
x = 7 + (-5)
x = 2
Therefore, the raw score corresponding to z = -1.25 is 2.
To find the raw score (X) corresponding to a given z-score, you can use the formula:
X = μ + (z * σ)
Where:
X = Raw score (the value you're trying to find)
μ = Mean of the distribution
z = Z-score (the given value)
σ = Standard deviation of the distribution
In this case, the mean (μ) is 7 and the standard deviation (σ) is 4. The given z-score is -1.25.
Plugging these values into the formula:
X = 7 + (-1.25 * 4)
X = 7 - 5
X = 2
Therefore, the raw score (X) corresponding to a z-score of -1.25 in this normal distribution with a mean of 7 and a standard deviation of 4 is 2.