Chapter 2.2, Problem 63E

To determine

20^th percentile of Mrs. Starnes’s Sudoku times for easy puzzles.

Answer to Problem 63E

20^th percentile is 4.544 minutes.

Explanation of Solution

Given information:

Mean, $\mu =5.3$

Standard deviation, $\sigma =0.9$

Calculations:

The data value represented by the x^th percentile has x% of the data values below it.

That implies

The data value represented by the 20^th percentile has 20% of the data values below it.

Now,

Find the z − score corresponding the probability of 20% (or 0.20) in the normal probability table of the appendix.

Note that

The closest probability would be 0.2005 that lies in the row -0.8 and in the column .04 of the normal probability table.

Then

The corresponding z − score,

  $z=-0.84$

In order to find x^thpercentile, 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,

20^th percentile will be 4.544 minutes.