Question

Which of the following is not true regarding the normal distribution?

• A. the point of inflecting are at $X=\mu \pm \sigma$
• B. skewness is zero
• C. maximum heigth of the curve is $\frac{1}{\sqrt{2\pi }}$
• D. mean $=$ media $=$ mode

Answer 1

Answer: (C)

maximum heigth of the curve is $\frac{1}{\sqrt{2\pi }}$

(i) Since $f\left(x\right)$ is a nonzero function we may divide both sides of the equation by this function. From this

it is easy to see that the inflection points occur where $X=\mu \pm \sigma$. In other words the inflection points are

located one standard deviation above the mean and one standard deviation below the mean

(ii)The skewness for perfect normal distribution is $0.0$. But if sample is greater than $100$ and less

than $200$, the acceptable absolute skewness value is $1.0$. However for large sample size n greater than $200$,

the absolute value for acceptable skewness is $15$.

(iii) The area under the normal curve is equal to $1.0$. Normal distributions are denser in the center and

less dense in the tails. Normal distributions are defined by two parameters, the mean $\left(\mu \right)$ and the standard

deviation $\sigma$. $68\%$ of the area of a normal distribution is within one standard deviation of the mean.

(iv) The mean, median, and mode of a normal distribution are equal. The area under the normal curve is equal to $1.0$. Normal distributions are denser in the center and less dense in the tails. Normal distributions are defined by two parameters, the mean (j) and the standard deviation (a).