An auditor randomly samples $20$ accounts receivable from among the $500$ such accounts of a

client$$s firm. The auditor lists the amount of each account and checks to see if the underlying

documents comply with stated procedures. The data are recorded in the accompanying table

$($amounts are in dollars, Y $=$ yes, and N $=$ no$).$

Account Amount Compliance Account Amount Compliance

$1278$ Y $11188$ N

$2192$ Y $12212$ N

$3310$ Y $1392$ Y

$494$ N $1456$ Y

$586$ Y $15142$ Y

$6335$ Y $1637$ Y

$7310$ N $17186$ N

$8290$ Y $18221$ Y

$9221$ Y $19219$ N

$10168$ Y $20305$ Y

Estimate the total accounts receivable for the $500$ accounts of the firm and place a bound on

the error of estimation. Do you think that the average account receivable for the firm exceeds

$$250?$ Why?