Question

A quality control inspector has drawn a sample of 1010 light bulbs from a recent production lot. If the number of defective bulbs is 22 or less, the lot passes inspection. Suppose 30%30% of the bulbs in the lot are defective. What is the probability that the lot will pass inspection? Round your answer to four decimal places.

Answer 1

To find the probability that the lot will pass inspection, we need to use the binomial distribution. The probability is approximately 0.9467.

Step-by-step explanation:

To find the probability that the lot will pass inspection, we need to find the probability that the number of defective bulbs in the sample is 22 or less. We can use the binomial distribution to calculate this probability. The binomial distribution is used when there are two possible outcomes, success or failure, and each trial is independent and has the same probability of success.

In this case, the probability of a bulb being defective is 30%. We have a sample size of 1010 bulbs. We want to find the probability that there are 22 or less defective bulbs. We can calculate this using the binomial cumulative distribution function (CDF).

We can use the formula P(x ≤ 22) = binomcdf(n, p, x) where n is the sample size, p is the probability of success, and x is the number of successes. In this case, n = 1010, p = 0.3, and x = 22.

Therefore, the probability that the lot will pass inspection is approximately 0.9467.