A sample has a mean of 120 and a standard deviation of 20.0. Find the value of x that corresponds to each of these standard scores:
a. z = 0.0
Z = 0 is always identical to the mean.
To find the value of x that corresponds to a standard score (z-score), you can use the formula:
x = μ + (z * σ)
where x is the value you're trying to find, μ is the mean, z is the standard score, and σ is the standard deviation.
In this case, you are given:
Mean (μ) = 120
Standard Deviation (σ) = 20.0
Standard Score (z) = 0.0
Using the formula, substitute the given values:
x = 120 + (0.0 * 20.0)
Since the standard score (z) is 0.0, multiplying it by the standard deviation (σ) would give us 0. So:
x = 120
Therefore, when the standard score (z) is 0.0, the corresponding value (x) is equal to the mean (μ), which is 120.