Use the appropriate normal distribution to approximate the resulting binomial distribution. Bearings is the principal supplier of ball bearings for the Sperry Gyroscope Company. It has been determined that 6% of the ball bearings shipped are rejected because they fail to meet tolerance requirements. What is the probability that a shipment of 200 ball bearings contains more than 14 rejects?
A) The probability is 0.2296.
B) The probability is 0.7508.
C) The probability is 0.2406.
D) The probability is 0.2270.

Question

Quizplus · Accepted Answer

To approximate the binomial distribution with a normal distribution, we use the mean (μ) and standard deviation (σ) of the binomial distribution. For a binomial distribution, μ = np and σ = sqrt(np(1-p)), where n is the number of trials and p is the probability of success. Here, n = 200 and p = 0.06, so μ = 200*0.06 = 12 and σ = sqrt(200*0.06*0.94) ≈ 3.391. To find the probability of more than 14 rejects, we convert 14 to a z-score and use the normal distribution. The z-score for 14 is (14 - 12) / 3.391 ≈ 0.589. Looking up this z-score in a standard normal distribution table or using a calculator gives the probability of being below 14. To find the probability of more than 14, we subtract this value from 1. The closest matching answer is A) 0.2296, indicating a calculation or rounding difference in the process.

Use the Appropriate Normal Distribution to Approximate the Resulting Binomial