All of the following statements are true about the normal distribution except:

The normal curve crosses the x-axis at z-scores above 3.0 and below -3.0.

The normal distribution is a mathematical model of a population distribution.

The total area under the normal curve is one.

The proportion of observations two standard deviations above the mean is the same as the proportion two standard deviations below the mean.

Values located on the normal curve are not meant as actual observations.

Question

All of the following statements are true about the normal distribution except:

       The normal curve crosses the x-axis at z-scores above 3.0 and below -3.0.

       The normal distribution is a mathematical model of a population distribution.

       The total area under the normal curve is one.

       The proportion of observations two standard deviations above the mean is the same as the proportion two standard deviations below the mean.

       Values located on the normal curve are not meant as actual observations.

paxpolaris · Answer

The normal curve crosses the x-axis at z-scores above 3.0 and below -3.0.
this is not true ... normal curve NEVER crosses x-axis

tkhunny · Answer

1) Why would probability be negative?
2) What?  Some populations may be normally distributed when measured by some criteria.
3) I hope so.  It is a fundamental requirement of a probability distribution.
4) This one is a little tricky.  The proportion of observations AT 2 SD above the mean is zero (0)!.  If it means "less than or equal to 2", then we should note that the the distribution is symmetric.
5) I can't even imagine what that means.