Final answer:
The false statement about normal distribution is that approximately 65% of the data lies within two standard deviations from the mean; the correct percentage is about 95% as per the Empirical Rule. Option d. approximately 65% of the data lies within 2 standard deviations from the mean is the correct answer.
Step-by-step explanation:
The student asked which of the following is not a property of a normal distribution:
- The area under the normal density curve must add up to 1
- The mean is equal to the median, and both lie directly in the middle of the curve
- Approximately 5% of the data lies outside 2 standard deviations from the mean
- Approximately 65% of the data lies within 2 standard deviations from the mean
- All are correct
The correct response is that approximately 65% of the data lies within 2 standard deviations from the mean. This statement is not true for the normal distribution. According to the Empirical Rule, about 95% of the data lies within 2 standard deviations from the mean in a normal distribution, not 65%. This is a commonly accepted fact about the characteristics of normal distributions and can be utilized to identify data patterns and make predictions in various disciplines such as statistics, science, and engineering.