Question

A company makes golf balls with painted logos in boxes of 100. The organization wants to construct a P-chart to track the percentage of golf balls with no logo in each sample. If the company used one box in each sample in the dataset, what is the sample standard deviation for the P-chart? Choose the closest answer. Sampledefects Sample defects Sample defects 8 9 10 15 16 17 18 19 20 TOTAL 2 4 2 12 13 14 6 72 a. 0.033 b. 0.072 C. 0.166 d. 0.019

Answer 1

Solution:

Defective rate, P-bar = Number of defects / Total Number of balls

Total number of balls = Number of samples x Number of boxes in each sample x Number of balls in each box

Total number of balls = 20 x 1 x 100 = 2,000

P-bar = 72 / 2,000

P-bar = 0.036

Sample Standard deviation for the p-chart (Sp) is calculated as,

Sp = SQRT [P-bar x (1 - P-bar)] / n

Sp = SQRT [0.036 x (1 - 0.036)] / 100

Sp = 0.0186 or 0.019 (Rounding off to three decimal places)

Standard deviation = 0.019