For a population with a standard deviation of s = 12, a z-score of z = +0.50 corresponds to a score that is above the mean by 6 points.
True or False
False.
A z-score is a measure of how many standard deviations a particular data point is from the mean. It is calculated using the formula: z = (X - μ) / σ, where X is the data point, μ is the mean, and σ is the standard deviation.
In this case, a z-score of +0.50 means that the data point is 0.50 standard deviations above the mean. Therefore, to find the score corresponding to this z-score, we can use the formula: X = μ + (z * σ).
In the question, it is stated that the standard deviation (σ) is 12, and the z-score (z) is +0.50. However, we do not have the information about the value of the mean (μ), so we cannot calculate the score (X) corresponding to this z-score. Therefore, it is not possible to determine whether the score is above the mean by 6 points or not.
True.
To determine whether the statement is true or false, we need to calculate the actual score corresponding to the given z-score.
Given that the standard deviation (s) is 12 and the z-score (z) is +0.50, we can use the formula z = (X - μ) / s, where X represents the score, μ represents the mean, and s represents the standard deviation.
Rearranging the formula to solve for X, we get X = μ + (z * s).
Plugging in the values, X = μ + (0.50 * 12).
Simplifying further, X = μ + 6.
This means that the score corresponding to a z-score of +0.50 is 6 points above the mean.
Since the statement in the question matches the calculated result, we can conclude that the statement is true.
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