Last year, a manufacturer produced 350,000 DVD players. Of these, approximately 1% were defective. Assume that a simple random sample of n = 140 players is drawn. Use the Poisson Approximation to the binomial distribution to compute the standard deviation of the number of DVD Players that were defective.
A) 1
B) 1.4
C) 48.3
D) 1.2

Question

Quizplus · Accepted Answer

First, we need to find the mean of the number of DVD players that are defective in a sample of 140.

Mean (µ) = np = 140*0.01 = 1.4

Next, we need to calculate the variance using the Poisson approximation:

Variance (σ^2) = npq = np(1-p) = 140*0.01*0.99 = 1.386

Finally, we take the square root of the variance to get the standard deviation:

Standard deviation (σ) = √(1.386) ≈ 1.18

Therefore, the closest option in the answer choices is D) 1.2.

Last Year, a Manufacturer Produced 350,000 DVD Players