Estimate the indicated probability by using the normal distribution as an approximation to the binomial distribution.
-With n = 18 and p = 0.30, estimate P(6).
A)0.1958
B)0.1239
C)0.8513
D)0.1015

Question

Quizplus · Accepted Answer

To estimate P(6) using the normal distribution as an approximation to the binomial distribution with n = 18 and p = 0.30, we first calculate the mean (μ) and standard deviation (σ) of the binomial distribution. The mean is μ = np = 18 * 0.30 = 5.4, and the standard deviation is σ = sqrt(np(1-p)) = sqrt(18 * 0.30 * 0.70) ≈ 2.07. To find P(6), we convert the binomial probability to a z-score and then use the normal distribution. The z-score for 6 is (6 - 5.4) / 2.07 ≈ 0.29. Looking up this z-score in a standard normal distribution table or using a calculator gives a probability close to the value in choice A, 0.1958.

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