91影视

Mean speed,$渭=112mph$

Standard deviation,$蟽=5mph$

The formula used:$z=\frac{x鈭�渭}{蟽}$

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 $z鈭�$score,

$z=1.04$

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

$z=\frac{x鈭�渭}{蟽}=\frac{x鈭�112}{5}$

Equate the above two expressions:

$\frac{x鈭�112}{5}=1.04$

Multiply both sides by $5:$

$x鈭�112=5.2$

Add $112$to both sides:

$x=5.2+112$

That becomes

$x=117.2$

Thus,

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