The standard deviation is $1\mathrm{.}5.$

Mean is $28$

Consider the activities for Project Respawn Flash shown in the $($partially incomplete$)$ table below, along with expected times and variances of times. Assume time is measured in hours.

$\backslash$table$[[$ACTIVITY$,$EXPECTED TIME,VARIANCE OF TIME$],[$A$,7,0\mathrm{.}11],[$B$,2,0\mathrm{.}80],[$C$,6,0\mathrm{.}22],[$D$,11,0\mathrm{.}43],[$E$,9,0\mathrm{.}11],[$F$,4,0\mathrm{.}22],[$G$,,],[$H$,6,1\mathrm{.}00]]$

Based on what you got in previous questions, answer the two questions below:

$($ii$)$ Find the probability that the project will take more than $26$ hours. $Pg($Give answer to the nearest percent$)$

Steps:

Find $z$ value : $z=\frac{x-\text{m}\text{e}\text{a}\text{n}}{?}$ sta sdard deviation; where $x$ is the target $(26)$

Find the probability or area under the curve on z$-$table for z$-$value found in step $1.$

Subtract the number from $1$ as we lok for the values greater than $26.$

$($iii$)$ Suggest a due date that gives the project a $88\%$ chance of on$-$time completion. $[$due$]$ hours. $($Give answer to one decimal.$)$

Steps:

Find $z$ score of $0\mathrm{.}88($look inside the $z$ table for $0\mathrm{.}88$ and read corresponding first column and first row$)$ and call it $z_{0\mathrm{.}88}.$

Calculate the target $(x)$ using: $x=$ mean $+z_{0\mathrm{.}88}**$ standard deviation.