Question

Ten percent of the items produced by a machine are defective. A random sample of 100 items is selected and checked for defects. Round answers to four decimal places.

A)What is the probability that the sample will contain more than 2.5% defective units?

B)What is the probability that the sample will contain more than 13% defective units?

Answer 1

P = proportion of defectives = 0.10
n = 100 ( sample size)

a)
Standard error of proportion = sqrt ( P(1-P) / n)
= sqrt ( (0.10)(0.90) / 100) = 0.03

b)
Let p^ be the sample proportion of defectives

P(p^ > 0.025) =

μ = 0.1
σ = 0.03
standardize x to z = (x - μ) / σ
P(x > 0.025) = P( z > (0.025-0.1) / 0.03)
= P(z > -2.5) = 0.9938
(From Normal probability table)

c)
P( p^ > 0.13)
μ = 0.1
σ = 0.03
standardize x to z = (x - μ) / σ
P(x > 0.13) = P( z > (0.13-0.1) / 0.03)
= P(z > 1) = 0.1587