Garbage trucks entering a particular waste$-$management

facility are weighed prior to offloading their contents.

Let X $5$ the total processing time for a randomly selected

truck at this facility $($waiting$,$ weighing, and offloading$).$

The article $$Estimating Waste Transfer Station Delays

Using GPS$($Waste Mgmt$.,2008$: $17421750)$ suggests

the plausibility of a normal distribution with mean

$13$ min and standard deviation $4$ min for X$.$ Assume that

this is in fact the correct distribution.

a$.$ What is the probability that a single truck$$s processing time is between $12$ and $15$ min?