A letter is mailed to a sample of 500 homeowners. Based on past experience, the probability of an undeliverable letter is 0.06. The normal approximation to the binomial probability of 40 or more undeliverable letters is:
A)0.9632
B)0.0368
C)0.2305
D)0.7695

Question

Quizplus · Accepted Answer

The normal approximation to the binomial distribution can be used here with the mean (μ) = np and the standard deviation (σ) = sqrt(np(1-p)), where n = 500 and p = 0.06. This gives μ = 30 and σ = sqrt(28.2) ≈ 5.31. To find the probability of 40 or more undeliverable letters, we calculate the z-score for 39.5 (continuity correction) as (39.5 - 30) / 5.31 ≈ 1.79. Looking up this z-score in the standard normal distribution table gives a tail probability of approximately 0.0368, indicating the probability of getting 40 or more undeliverable letters is 0.0368.

A Letter Is Mailed to a Sample of 500 Homeowners