Question

Lee is a cadet at the Honolulu Police Academy. He was asked to make a P-Chart for reported (minor) property crimes. Lee chose a small neighborhood with 481 families. Each family is viewed as a binomial trial. Success means that the family was the victim of at least one minor property crime in the past 3 months. Police reports gave the following data for the past 12 quarters (4 years). Assume the 481 families lived in the neighborhood all 4 years.

Quarter	1	2	3	4	5	6
r = no. of successes	11	14	18	23	19	15
p̂ = r / 481	0.02	0.03	0.04	0.05	0.04	0.03

Quarter	7	8	9	10	11	12
r = no. of successes	12	16	13	22	24	19
p̂ = r / 481	0.02	0.03	0.03	0.05	0.05	0.04

Make a P-Chart. (Use 4 decimal places.)

Center line	=
–2.0 SL	=
2.0 SL	=
–3.0 SL	=
3.0 SL	=

List any out-of-control signals by type (I, II, or III). (Select all that apply.)

Out-of-control signal I occurs on Quarter 11.There are no out-of-control signals.Out-of-control signal III occurs on Quarter 1.Out-of-control signal III occurs on Quarter 7.

Answer 1

number of samples m=					12.00
sample size n=					481.00
total number of units =mn=					5772.00
number of defects d =					206.00
hence non conforming fraction p̅=d/(mn)=					0.0357

standard error =√(p*(1-p)/n) =0.0085

control line (CL) = p̅=

0.0357

-2.0SL = 0.0357-2*0.0085 =0.0188

2SL =0.0357+2*0.0085 =0.0526

-3.0SL = 0.0357-3*0.0085 =0.0103

3.0SL =0.0357+3*0.0085 =0.0611

.There are no out-of-control signals