For a sample with a mean of M=85, a score of X=90 corresponds to a z-score of z=1.00. What is the sample standard deviation?
Since (Score-Mean)= 90 - 85
= z*(std. deviation) = 5 ,
std. deviation = 5/z = 5/1.00 = 5
To find the sample standard deviation, we can use the formula:
z = (X - M) / σ
Given that for a score of X = 90, the corresponding z-score is z = 1.00, we can solve the equation as follows:
1.00 = (90 - 85) / σ
Substituting the values, we have:
1.00 = 5 / σ
To solve for σ, we can cross-multiply:
σ = 5 / 1.00
Therefore, the sample standard deviation is σ = 5.
To find the sample standard deviation, we can use the formula:
z = (X - M) / σ
Where:
- z is the z-score
- X is the score
- M is the mean
- σ is the standard deviation
We are given that the score X is 90 and the z-score is 1.00. We also know that the mean is M = 85.
Plugging in these values into the formula, we get:
1.00 = (90 - 85) / σ
To solve for σ (the standard deviation), we can rearrange the equation:
1.00 * σ = 90 - 85
σ = 5
Therefore, the sample standard deviation is 5.