Estimate the indicated probability by using the normal distribution as an approximation to the binomial distribution.
-With n = 20 and p = 0.60, estimate P(fewer than 8).
A) 0.0668
B) 0.4953
C) 0.0202
D) 0.4332

Question

Quizplus · Accepted Answer

To use the normal approximation, calculate the mean (μ = np = 20*0.60 = 12) and standard deviation (σ = √(np(1-p)) = √(20*0.60*0.40) = √4.8 ≈ 2.19). For P(X < 8), use continuity correction: P(X < 7.5). Convert to z-score: z = (7.5 - 12) / 2.19 ≈ -2.05. Using z-tables, P(Z < -2.05) ≈ 0.0202.

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