91Ó°ÊÓ

Mean,$\mathrm{μ}=5.3$

Standard deviation,$\mathrm{σ}=0.9$

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 $20th$ percentile represents a data value with $20\%$ 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 $20\%$ (or $0.20$).

Note that

The probability that comes closest is $0.2005$which is found in row $-0.8$ and column$.04$ of the normal probability table.

Then

The corresponding $z−$ score,

$z=−0.84$

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

$z=\frac{x−\mathrm{μ}}{\mathrm{σ}}=\frac{x−5.3}{0.9}$

Equate the above two expressions:

$\frac{x−5.3}{0.9}=−0.84$

Multiply both sides by $0.9$

$x−5.3=−0.756$

Add $5.3$ to both sides:

$x=−0.756+5.3$

That becomes

$x=4.544$

Thus,

$20th$ percentile will be $4.544$ minutes.