$[[$Engineering Statistics: Please show all work and define all variables, so I can check mine! Thank you! $]]$

Bed$-$material sediment particle size data are critical for understanding riverine sediment transport. Particularly the median particle size $($D$50)$ and $85$th percentile particle size $($D$85)$ values are commonly used in the design of river restoration projects. A sample of $15$ observations of particle size X$($in mm$)$ at a location are provided below, sorted in an order of smallest to largest values:

$1\mathrm{.}3911\mathrm{.}6901\mathrm{.}7231\mathrm{.}7791\mathrm{.}8871\mathrm{.}9742\mathrm{.}1442\mathrm{.}153$

$2\mathrm{.}1602\mathrm{.}1872\mathrm{.}7383\mathrm{.}7903\mathrm{.}9894\mathrm{.}4985\mathrm{.}493$

The mean of X is $2\mathrm{.}640$ mm and the standard deviation is $1\mathrm{.}217$ mm$,$ respectively.

a$)$ Compute the sample coefficient of variation.

Using the plotting position formula, compute:

b$)$ Empirical CDF of X

c$)$ Pr $($X $>2\mathrm{.}000$ mm$)$

d$)$ D$50$

e$)$ D$85$