Problem $2.$ At Trustco Bank, the Data & Statistics Department $($DSD$)$ is responsible for transferring the

data on paperwork to the Bank$$s information system. The department$$s supervisor takes a sample of $144$

records of data everyday, and has them checked in order to determine whether there is any errors made

on the record. Any record that contains one or more errors $($e$.$g$.,$ typos$)$ is considered defective. The

following numbers of defective data records are found. Is the data entry process in control? Use three$-$

sigma control limits$.$

Sample Defective

Records

$13$

$25$

$33$

$44$

$52$

$64$

$72$

$86$

$94$

$107$

$112$

$126$

$135$

$141$

$155$

$160$

$172$

$186$

$192$

$203$