E$=\{8,11,16,20,27,36,42,46,52,55,78,86,96,108,123\}$

a$)$ Calculate the mean $\backslash$mu E and the standard deviation $\backslash$sigma E of the given numbers $($E$).$

b$)$ Using the following equation and the calculated mean $\backslash$mu E and standard deviation $\backslash$sigma E$,$calculate

each f$($E$)$ value that corresponds to each E$.$

c$)$ Plot the distribution as an E against f$($E$)$ graph.

d$)$ Calculate the mean $\backslash$mu and the standard deviation $\backslash$sigma of the f$($E$)$ data you generated.

e$)$ Find the probabilities corresponding to each z value using the probability distribution function $($normal distribution$)$ table.

f$)$ Plot the probabilites obtained from the table against f$($E$)$ to form a normal probability paper plot. Plot a trendline to more clearly see the linearity.

g$)$ From the normal probability paper plot you obtained, again find the mean and the standard deviation of the f$($E$)$ data.

h$)$ Calculate the skewness coefficient of the f$($E$)$data$.$a$)$ Calculate the mean ${}_{}$ and the standard deviation ${}_{}$ of the given numbers $().$

b$)$ Using the following equation and the calculated mean ${}_{}$ and standard deviation ${}_{},$calculate

each $f()$ value that corresponds to each $.$

$f()=\frac{1}{{}_{}\sqrt[\phantom{2}]{2}}{e}^{\frac{-(-{}_{}{)}^2}{2{}_{}^2}}$

c$)$ Plot the distribution as an $$ against $f()$ graph.

$($In this wav, vou have generated vour own normal distribution data $f(),$ using which, vou will do all

the following normal distribution calculations.

d$)$ Calculate the mean $$ and the standard deviation $$ of the $f()$ data you generated.

Subsequently, calculate the standardized variable $z$ for each $f()$ value

e$)$ Find the probabilities corresponding to each $z$ value using the probability distribution

function $($normal distribution$)$ table

f$)$ Plot the probabilites obtained from the table against $f()$ to form a normal probability paper

plot. Plot a trendline to more clearly see the linearity.

g$)$ From the normal probability paper plot you obtained, again find the mean and the standard

deviation of the $f()$ data

h$)$ Calculate the skewness coefficient of the $f()$ data.