Answer
The guaranteed time limit should be 22 minutes.
(Image below can aid in working)
Work Step by Step
$\mu$ =17, $\sigma$ = 2.5
If the time required to complete an oil change service exceeds $x$ minutes, then speedy lube will have to give the discount to 3% of its customers.
To find $x$
i ) z- score corresponding to an area of 0.97 = 1.88
ii) Sub $\sigma = 2.5 , \mu= 17, z = 1.88$ into z = $\frac{x - \mu}{\sigma}$ and solve for x:
z = $\frac{x - \mu}{\sigma}$
$x$ = $\mu$ + $z\sigma$
$x$ = $17 + (1.88 \times 2.5)$
$x$ = $21.7$
$x$ $\approx$ 22 minutes
