Question

Dawson’s Repair Service orders parts from an electronic company, which advertises its parts to be no more than 2% defective. What is the probability that Bill Dawson finds three or more parts out of a sample of 50 to be defective? Use Appendix B.1 for the z-values. (Round the z-value to 2 decimal places and the final answer to 4 decimal places.)

Answer 1

To find the probability that Bill Dawson finds three or more defective parts out of a sample of 50, we can use the binomial probability formula. The formula is: P(X >= k) = 1 - P(X < k-1).

Step-by-step explanation:

To find the probability that Bill Dawson finds three or more defective parts out of a sample of 50, we can use the binomial probability formula. The formula is:

P(X >= k) = 1 - P(X < k-1)

In this case, k is 3, since we want to find the probability of three or more defective parts. P(X < k-1) is the cumulative probability of having less than (k-1) defective parts. Using the binomial probability formula, we can calculate the cumulative probability and subtract it from 1 to find the desired probability.

Answer 2

The probability that there will be three or more defective parts in a sample of 50 pieces, with a defect rate of 2%, is determined using normal approximation to the binomial distribution. The resulting z-value is extremely high, indicating that such an event is very unlikely.

Step-by-step explanation:

The question asks about the probability that in a sample of 50 parts from an electronic company, with a defect rate of no more than 2%, there will be three or more defective parts. To solve this, we can use the normal approximation to the binomial distribution because we have a large sample size and a small probability of success (defect rate).

We first find the mean (μ) and standard deviation (σ) for the number of defective parts:

μ = np = 50(0.02) = 1
σ = √(np(1-p)) = √(50(0.02)(0.98)) ≈ 0.14

Next, we standardize the variable to find the z-value. Since we are looking for the probability of finding three or more defective parts, we need to find P(X ≥ 3). We use 2.5 as the continuity correction factor.

Standardizing, the z-value is calculated as follows:

z = (x - μ)/σ = (2.5 - 1) / 0.14 ≈ 10.71

The z-value is very high, which suggests that P(X ≥ 3) is extremely small. To find the exact probability, we'd consult the z-table in Appendix B.1 and look for the corresponding probability value or use statistical software.

Since the probability associated with such a high z-value is nearly zero, we can say the probability of finding three or more defective parts is very unlikely assuming the defect rate is indeed 2%.