Determine if the following statement is true or false. The normal curve is symme

Question

Determine if the following statement is true or false. The normal curve is symmetric about its mean, mu. Choose the best answer below. A. The statement is false. The mean is the balancing point for the graph of a distribution, and therefore, it is impossible for any distribution to be symmetric about the mean. B. The statement is true. The mean is the balancing point for the graph of a distribution. and therefore, all distributions are symmetric about the mean. C. The statement is true. The normal curve is a symmetric distnbution with one peak, which means the mean, median, and mode are all equal. Therefore, the normal curve is symmetric about the mean, mu. D. The statement is false. The normal curve is not symmetric about its mean, because the mean is the balancing point of the graph of the distribution. The median is the pointt where 50% of the area under the distribution is to the left and 50% to the right. Therefore, the normal Curve could only be symmetric about its median, not about its mean.

Explanation / Answer

here the discussion says that the curve is symterric

But we dont know whether is it about its mean or Not.

The normal curve is symetric means that there is no skewness.

Though there maybe kurtosis,still it can be symetteric

If the curve is symettric,the mean=median=mode

The peak of the curve occurs at the mode.and it is symettric about the mode

and yes about the median 50% and 50% are distributed.

Option A) is wrong as the distribution can be symetric about its mean.

Option B) is wrong as all distributions need not be symetric about the mean.

Option D) the normal curve is symetric about the mode,not only the median.Hence it is wrong.

Hence Option C) is true

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