Tells how many standard deviations a value is from the mean; if you have a mean of zero then you have a standard deviation of one

Tells how many standard deviations a value is from the mean; if you have a mean of zero then you have a standard deviation of one

• A. The probability of observing the value.
• B. The mean value.
• C. The area under the curve up to the value.
• D. The number of standard deviations a value is from the mean

Answer: (D)

This question is about the z-score, a standard score that tells you how many standard deviations a value is from the mean. It’s defined as z = (X − μ)/σ, where μ is the mean and σ is the standard deviation. This measures deviation in units of standard deviation, which is exactly what the statement describes: how far, in terms of standard deviations, a value lies from the mean. In a standard normal distribution, the mean is 0 and the standard deviation is 1, so the z-score simplifies to z = (X − 0)/1 = X. That means the value itself equals its number of standard deviations away from the mean. The other descriptions refer to probability-related quantities—the probability of observing the value is about likelihood, while the area under the curve up to the value is the cumulative probability (CDF). The mean value is just the center of the distribution, not a measure of deviation.

This question is about the z-score, a standard score that tells you how many standard deviations a value is from the mean. It’s defined as z = (X − μ)/σ, where μ is the mean and σ is the standard deviation. This measures deviation in units of standard deviation, which is exactly what the statement describes: how far, in terms of standard deviations, a value lies from the mean.

In a standard normal distribution, the mean is 0 and the standard deviation is 1, so the z-score simplifies to z = (X − 0)/1 = X. That means the value itself equals its number of standard deviations away from the mean.

The other descriptions refer to probability-related quantities—the probability of observing the value is about likelihood, while the area under the curve up to the value is the cumulative probability (CDF). The mean value is just the center of the distribution, not a measure of deviation.