Which of the following is not true regarding the normal distribution?
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A. B. C. D. E.Explanation
Nothing is stated about the points where the curve meets the X axis (does it meet at all?)
The correct answer is C. None of these answers.
Let's go through each option to understand why it is true or false:
A. It is symmetrical: This statement is true. The normal distribution is symmetric, which means that the left and right sides of the distribution are mirror images of each other. The mean of the distribution is located at the center, and the probabilities of observing values to the left and right of the mean are equal.
B. It has a single peak: This statement is true. The normal distribution is unimodal, which means it has a single peak. The highest point of the curve corresponds to the mean of the distribution.
C. None of these answers: This option is incorrect. Both options A and B are true, as explained above. Therefore, option C is not the correct answer.
D. Mean, median, and mode are all equal: This statement is true. In a normal distribution, the mean, median, and mode are all equal. This occurs because of the symmetry of the distribution. The mean is the average of all data points, the median is the middle value when the data is arranged in ascending order, and the mode is the most frequently occurring value. Since the normal distribution is symmetrical, these three measures of central tendency coincide and are equal.
E. The points of the curve meet the X-axis at z = -3 and z = 3: This statement is false. In a standard normal distribution (a specific type of normal distribution with a mean of 0 and a standard deviation of 1), the points on the curve meet the X-axis (or z-axis) at z = -3 and z = 3. However, the statement does not specify that it is referring to a standard normal distribution. In a general normal distribution, the points where the curve meets the X-axis will depend on the specific mean and standard deviation of that distribution.
Therefore, the correct answer is C. None of these answers, as options A, B, and D are all true statements regarding the normal distribution, while option E is false or incomplete depending on the context.