Which chart to use? Respond with which chart$($s$)($X$-$bar, R$,$ s$,$ p$,$ c$,$ u$)$ could apply in each

setting and offer a brief justification $(1$ sentence$).$

$($a$)(4$pts$)$ Hospital Infection Rates. A hospital tracks the rate of post$-$operative infections among

patients to ensure quality and safety in surgical procedures. They collect data on the number

of infections per $100$ surgeries conducted each month. Which control chart$($s$)$ should they

use to monitor infection rates effectively?$/$Why$?$

$($b$)(4$pts$)$ Automotive Assembly Line. An automotive manufacturer wants to ensure that the

dimensions of car doors are consistent with design specifications. Measurements are taken

from a sample of $10$ doors each day to monitor the average dimensions and variation. Which

control chart$($s$)$ would be best suited for this purpose?$/$Why$?$

$($c$)(4$pts$)$ Call Center Service Levels. A call center measures the number of calls that are

dropped due to technical issues out of the total calls received each day. They aim to monitor

and reduce the proportion of dropped calls to improve customer satisfaction. Which control

chart is most appropriate for monitoring this aspect of service quality?$/$Why$?$

$($d$)(4$pts$)$ Electronics Component Manufacturing. In manufacturing electronic components, a

company inspects the number of defective transistors in batches of $500.$ They seek to

monitor and control the quality by tracking the count of defects. Which control chart should

be used for this purpose?$/$Why$?$

$($e$)(4$pts$)$ Beverage Bottling Process. A beverage company wants to monitor the consistency

of liquid volume filled in $2-$liter bottles to ensure they meet the labeled volume. Samples

of bottles with variable sizes are taken hourly, and the volume is measured. The company

wishes to monitor both the average fill volume and variability. Which control charts would be

appropriate?$/$Why$?$