91Ó°ÊÓ

Mean speed,$\mathrm{μ}=112mph$

Standard deviation,$\mathrm{σ}=5mph$

The formula used:$z=\frac{x−\mathrm{μ}}{\mathrm{σ}}$

The $Xth$percentile represents a data value with $x$percent of the data values below it.

That implies

The $85th$percentile represents a data value with$85$ percent of the data values below it.

Now,

In the normal probability table of the appendix, find the $z-$score that corresponds to a probability of $85$ percent (or $0.85$).

Note that

The closest probability would be $0.8508$ which lies in row $1.0$ and in column $.04$ of the normal probability table.

Then

The corresponding $z−$score,

$z=1.04$

In order to find the $xth$ percentile, calculate the $z−$score

$z=\frac{x−\mathrm{μ}}{\mathrm{σ}}=\frac{x−112}{5}$

Equate the above two expressions:

$\frac{x−112}{5}=1.04$

Multiply both sides by $5:$

$x−112=5.2$

Add $112$to both sides:

$x=5.2+112$

That becomes

$x=117.2$

Thus,

$85th$percentile will be $117.2$mph.