Question

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

Answer 1

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