Find the standard deviation...

Question

The quality- control inspector of a production plant will reject a batch of syringes if two or more defective syringes are found in a random sample of twelve syringes taken from the batch. Suppose the batch contains 1% defective syringes.

Find σ( in terms of the number of syringes). ( enter a number. Round your answer to three decimal places.)

Answer 1

Question: The quality- control inspector of a production plant will reject a batch of syringes if two or more defective syringes are found in a random sample of twelve syringes taken from the batch. Suppose the batch contains 1% defective syringes.

Find σ (in terms of the number of syringes). (Enter a number. Round your answer to three decimal places.)

Answer: Let's think of the number of syringes being defective as a binomial random variable. It's either defective, or it's not. Also, we count syringes with counting numbers (0, 1, 2, etc.). A binomial random variable is a kind of discrete random variable.

We're given that in the batch, there can be assumed to be 1% defective syringes. Let's say that n=12 (for 12 syringes in our sample), p = 0.01, and let's say that q = 1 - p = 0.99. Respectively, these are probabilities of success and of failure for a single syringe ("success" here is being defective).

The formula for the standard deviation of a binomial random variable is σ = sqrt(npq).

σ = sqrt(12 * 0.01 * 0.99)

σ = sqrt(0.1188)

σ ≈ 0.345

The standard deviation is approximately 0.345 syringes.