At the Bright Idea Lighting Company $10$ flashlights are sampled each hour to determine whether the manufacturing process is in control. The UCL is $0.10$ defective, and the LCL is $0.05$ defective.

1. Create a process control chart for the following hours.

   Hour	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$	$12$	$13$
   proportion defective	$0.06$	$0.08$	$0.09$	$0.06$	$0.05$	$0.08$	$0.08$	$0.07$	$0.11$	$0.10$	$0.05$	$0.07$	$0.04$

   Hour	$14$	$15$	$16$	$17$	$18$	$19$	$20$	$21$	$22$	$23$	$24$	$25$
   proportion defective	$0.08$	$0.08$	$0.09$	$0.08$	$0.09$	$0.09$	$0.08$	$0.09$	$0.10$	$0.06$	$0.05$	$0.05$	checksum $1.88$

   Hint (a):

   Place the 'hours' on the $x$-axis and the 'proportion defective' on the $y$-axis. Scale the $y$-axis from $0.05$ to $0.10$.

2. As a quality control engineer for Bright Idea, what do you report about the process control?

   Hint (b):

   Draw a centerline at $y = 0.075$ on your graph.
   Comment on how close/far the points are relative to the centerline.
   What about several points in a row staying above/below the centerline?