MATH SOLVE

8 months ago

Q:
# If a data value in a normal distribution has a negative z-score, which of the following must be true?The data value must be negative.The data value must be positive.The data value must be less than the mean.The data value must be greater than the mean.

Accepted Solution

A:

Correct Answer:

The data value must be less than the mean.

The formula for the z value is:

z-value = (Data value - Mean) / Standard Deviation

The z-value will be negative when the Numerator of the above expression will be negative. The numerator will be negative only when the Data Value is less than the mean value. For example, for a data value of 5 and mean value 8, the numerator will be -3, and when it will be divided by standard deviation, the resulting z value will be negative.

So, Third option is the correct answer.

The data value must be less than the mean.

The formula for the z value is:

z-value = (Data value - Mean) / Standard Deviation

The z-value will be negative when the Numerator of the above expression will be negative. The numerator will be negative only when the Data Value is less than the mean value. For example, for a data value of 5 and mean value 8, the numerator will be -3, and when it will be divided by standard deviation, the resulting z value will be negative.

So, Third option is the correct answer.