Use the normal distribution to approximate the desired probability.
-Find the probability that in 200 tosses of a fair die, we will obtain at exactly 30 fives.
A) 0.1871
B) 0.0429
C) 0.0871
D) 0.0619

Question

Quizplus · Accepted Answer

To approximate the probability using a normal distribution, we use the binomial distribution parameters: n = 200, p = 1/6. The mean (μ) is np = 200*(1/6) = 33.33 and the standard deviation (σ) is sqrt(np(1-p)) = sqrt(200*(1/6)*(5/6)) ≈ 5.27. Using the continuity correction, we find P(29.5 < X < 30.5) and convert to the standard normal distribution to find the probability, which is approximately 0.0619.

Use the Normal Distribution to Approximate the Desired Probability