Estimate the indicated probability by using the normal distribution as an approximation to the binomial distribution. Two percent of hair dryers produced in a certain plant are defective. Estimate the probability that
Of 10,000 randomly selected hair dryers, at least 219 are defective.
A) 0.0934
B) 0.0823
C) 0.0869
D) 0.9066

Question

Quizplus · Accepted Answer

Using the normal approximation to the binomial distribution, we find the mean (μ = np = 10,000 * 0.02 = 200) and standard deviation (σ = √(np(1-p)) = √(10,000 * 0.02 * 0.98) ≈ 14). We then calculate the z-score for 218.5 (continuity correction) and find the probability that z is greater than this value, which is approximately 0.0934.

Estimate the Indicated Probability by Using the Normal Distribution as an Approximation