For a p-chart,the standard deviation of the proportions is 0.066933.The number of items in each sample is 45.Then p is ______.
A)There is not enough information to determine p
B)0)25
C)0)28
D)0)32

Question

Quizplus · Accepted Answer

The formula for the standard deviation of proportions in a p-chart is:

σp = √[(p*q)/n]

where p is the proportion of nonconforming items, q = 1-p, and n is the number of items in the sample.

We are given that the standard deviation of proportions, σp = 0.066933, and n = 45.

Solving for p, we get:

σp = √[(p*q)/n]
0.066933 = √[(p*(1-p))/45]
0.066933^2 = (p*(1-p))/45
0.002243441 = p*(1-p)
0.002243441 = -p^2 + p
p^2 - p + 0.002243441 = 0

Using the quadratic formula, we can solve for p:

p = [1 ± √(1 - 4*1*0.002243441)]/2
p ≈ 0.028 or p ≈ 0.972

Since p represents the proportion of nonconforming items, it cannot be greater than 1 (or 100%). Therefore, we can discard the solution of p ≈ 0.972.

Thus, the value of p is approximately 0.028, which corresponds to choice C) 0.28 after multiplying by 100 to convert to percentage.

For a P-Chart,the Standard Deviation of the Proportions Is 0