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Q: Is it true or false that The area under a normal distribution curve is always positive even if the z value is negative?

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The Z value is negative, but area is always positive.

The normal distribution is always continuous.

No.

The distribution of sample means will not be normal if the number of samples does not reach 30.

The statement is false. The binomial distribution (discrete) or uniform distribution (discrete or continuous) are symmetrical but they are not normal. There are others.

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Neither. It is symmetrical.

The Z value is negative, but area is always positive.

The variance is always positive. The variance is not directly related to the sign (nor magnitude) of the mean.

It means distribution is flater then [than] a normal distribution and if kurtosis is positive[,] then it means that distribution is sharper then [than] a normal distribution. Normal (bell shape) distribution has zero kurtosis.

The normal distribution is always continuous.

Use the context: if the variable should be greater than the mean then z is positive and if less than the mean, it should be negative.

Yes, the normal distribution, standard or not is always continuous.

Yes.

A normal distribution can have any value for its mean and any positive value for its variance. A standard normal distribution has mean 0 and variance 1.

No. The variance of any distribution is the sum of the squares of the deviation from the mean. Since the square of the deviation is essentially the square of the absolute value of the deviation, that means the variance is always positive, be the distribution normal, poisson, or other.

Negative 5. It's normal division, except you need to remember these rules: Positive & Negative = Negative Positive & Positive = Positive

The normal distribution can have any real number as mean and any positive number as variance. The mean of the standard normal distribution is 0 and its variance is 1.

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