🎴 Flashcard Mode

$\left(i\right)$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

$\left(ii\right)$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 $1.5$.

$\left(iii\right)$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 $\left(\sigma\right)$. $68\%$ of the area  of a normal distribution is within one standard deviation of the mean.

$\left(iv\right)$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 $\left(\mu\right)$ and the standard deviation $\left(\sigma\right)$.