Question

Sudoku Refer to Exercise $61$Find the $20th$percentile of Mrs. Starnes’s

Sudoku times for easy puzzles.

Short answer

$20th$ percentile is $4.544$ minutes.

Step-by-step solution

Given information

Mean,$\mu =5.3$

Standard deviation,$\sigma =0.9$

Concept

The formula used:$z=\frac{x-\mu }{\sigma }$

Calculation

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

$z=\frac{x-\mu }{\sigma }=\frac{x-5.3}{0.9}$

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.