Mean = $231
Standard deviation = $5

Long ago, a Russian mathematician named

Пафну́тий Льво́вич Чебышёв
Pafnuty Lvovich Chebyshev (1821-1894)

came up with a formula for finding what percentage of any set 
of numbers must lie close to the mean.

In particular for any positive number k, the percentage of the 
data that lies within k standard deviations of the mean is at 
least  changed to a percent.

First we need to find out how many standard deviations $219 and 
$243 are from the mean of $231.  We subtract to find which, if 
either, of the two bounds, $219 and $234, is closer to the mean. 

$231-$219=$12
$243-$231=$12

(If those hadn't been the same we would have picked the smaller.)
we find that both limits are $12 from the mean.  Now we want to see
how many standard deviations this $12 difference is.  So we divide
by the given standard deviation, $5, to find out:

$12÷$5 = 2.4 = k standard deviations from the mean

So we want to know at least what percentage of the data must fall
within 2.4 standard deviations of the mean.  So we plug 2.4 for k
in Chebyshev's formula:







Now we change that to a percent.  So at least 82.6% of the data 
must fall within 2.4 standard deviations of the mean, and that 
tells us that at least 82.6% of the data must fall between 
$219 and $243.

Edwin