Which of the following is not a property of the normal distribution? a. the area under the normal density curve must add up to 1 b. the mean is equal to the median, and both lie directly in the middle of the curve c. approximately 5% of the data lies outside 2 standard deviations from the mean d. approximately 68% of the data lies within 2 standard deviations from the mean e. all are correct

The correct option is D.

Step-by-step explanation:

Consider the provided information.

Normal distribution is where the data tends to be around a central value.

The value of mean = median = mode

68% of data are within the 1 standard deviation of mean, 95% of data are within the 2 standard deviation of mean, and 99.7% of data are within the 1 standard deviation of mean. Also area under the normal curve is equals to 1.

Now consider the provided options.

Option A and B are the property of normal distribution. So they can't be the correct option.

Option c) Approximately 5 % of the data lies outside 2 standard deviations from mean.

From the above information we know that 95% data are within the 2 standard deviation, that means 100%-95%=5% of the data lies outside 2 standard deviations.

Hence, this option is incorrect

Option D) Approximately 68% of the data lies WITHIN 2 standard deviations from the mean.

68% data lies within 1st standard deviation, thus it is not a property of the normal distribution.

Hence, Option D) Approximately 68% of the data lies WITHIN 2 standard deviations from the mean is correct.

Option e) All are correct

This is an incorrect option because three of the choices are a property of the normal curve.

check the picture below.

f(x) is the value of the function. b is the value of the function when x equals zero or the y-coordinate of the point where the line crosses the y-axis in the coordinate plane.

step-by-step explanation:

hope this !