A random sample of 50 units is drawn from a production process every half hour. the fraction of nonconforming product manufactured is 0.02. what is the probability that?̂0.04 if the fraction nonconforming really is 0.02

To solve this problem, we solve for the z score of proportions. Using the formula:

z = (p1 - p2) / sqrt [ (p2 (1 - p2) / n) ]

where,

p1 = 0.04

p2 = 0.02

n = 50

Therefore:

z = (0.04 - 0.02) / sqrt [ (0.02 (1 - 0.02) / 50) ]

z = 1.01

From the standard probabilities table, the p value for this right tailed test at z = 1.01 is:

P = 0.1562

Therefore there is a probability of 0.1562 or 15.62% that the nonconforming would be 0.04 and above