It is true. Because the normal distribution is above the horizontal axis for all values, the area under it is a positive quantity no matter the z value.
The Z value is negative, but area is always positive.
The normal distribution is always continuous.
The distribution of sample means will not be normal if the number of samples does not reach 30.
No.
The statement is false. The binomial distribution (discrete) or uniform distribution (discrete or continuous) are symmetrical but they are not normal. There are others.
The Z value is negative, but area is always positive.
Neither. It is symmetrical.
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.
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.
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.
The normal distribution is always continuous.
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.
Negative 5. It's normal division, except you need to remember these rules: Positive & Negative = Negative Positive & Positive = Positive
Yes, the normal distribution, standard or not is always continuous.
Yes.
When you divide or multiply positive and negative numbers, you first do the division or multiplication as normal. The next step is to assess whether or not the answer will be negative or positive. If the two numbers of the question were the same (negative and negative or positive and positive) then the answer will be positive. If the two numbers in the question were different (one negative and one positive) then the answer will be negative. Thus, if you divide a negative number by a positive number, the result will be the same as normal division, but the answer will be negative.