Problem $1.$

$(1$ point$)$ Caitlin Elizabeth is studying task completion times at Gordon's Freight Company $($Gordon$\text{'}$s$)$ for the purpose of improving the company's ability to estimate task times. Building a project simulator is an important part of Caitlin's work.

The table below shows an empirical distribution Caitlin prepared for a common task:

$\backslash$footnotesize $\backslash$baselineskip $=12$pt

$\backslash$begin$\{$tabular$\}\{$c $|$ c$\}$

t & Pr $\backslash$lbrace T $=$ t $\backslash$rbrace $\backslash \backslash \backslash$hline

$14$ & $0\mathrm{.}08\backslash \backslash 18$ & $0\mathrm{.}3\backslash \backslash 20$ & $0\mathrm{.}1\backslash \backslash 22$ & $0\mathrm{.}2\backslash \backslash 67$ & $0\mathrm{.}32\backslash \backslash$

$\backslash$end$\{$tabular$\}$

Given the following U ~ unif$[0,1],$ calculate a random task duration that follows the given discrete distribution:

Please enter your answers as whole numbers:

U $=0\mathrm{.}2547\backslash$Rightarrow X $=$