Question

Which of the following is not a characteristic of the normal probability distribution?

Group of answer choices
The mean is equal to the median, which is also equal to the mode.
The total area under the curve is always equal to 1.
99.72% of the time the random variable assumes a value within plus or minus 1 standard deviation of its mean
The distribution is perfectly symmetric.

Answer 1

The normal probability distribution is characterized by the mean, median, and mode being equal, the total area under the curve being 1, and approximately 99.72% of the values falling within plus or minus 1 standard deviation of the mean. The distribution is not perfectly symmetric.

Step-by-step explanation:

The normal probability distribution has several characteristics:

1. The mean, median, and mode are equal, making the distribution symmetric.
2. The total area under the curve is always equal to 1.
3. Approximately 99.72% of the time, the random variable assumes a value within plus or minus 1 standard deviation of its mean.

Therefore, the characteristic that is NOT true of the normal probability distribution is that the distribution is perfectly symmetric.

Answer 2

The incorrect statement about the normal probability distribution is that '99.72% of the time the random variable assumes a value within plus or minus 1 standard deviation of its mean', while the empirical rule states approximately 68% of data falls within one standard deviation of the mean.

Step-by-step explanation:

The question pertains to characteristics of the normal probability distribution. Among the given statements, the one that is not characteristic of the normal distribution is that '99.72% of the time the random variable assumes a value within plus or minus 1 standard deviation of its mean'. This is incorrect because according to the empirical rule (or the 68-95-99.7 rule), approximately 68% of the data falls within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations in a normal distribution.

The key characteristics of a normal distribution are that it is symmetric about the mean, the total area under the curve equals to 1, and the mean, median, and mode are all equal. It also never touches the x-axis, maintaining an asymptotic relationship with it.