4. Continuous Distributions

Normal Approximation — Quiz

Test your understanding of normal approximation with 5 practice questions.

Practice Questions

Question 1

When 120 fair six-sided dice are rolled, approximate the probability that the sum exceeds 435 using a normal approximation.

Question 2

For $X\sim\mathrm{Binomial}(200,0.4)$, approximate $P(X<90)$ using a normal approximation with continuity correction.

Question 3

A random sample of size $n=64$ is drawn from $N(\mu=65,\sigma=8)$. What is $P(63<\overline X<67)$?

Question 4

For a rare event with true defect rate $p=0.02$, what minimum sample size $n$ ensures the normal approximation to $\mathrm{Binomial}(n,0.02)$ is appropriate under $n p\ge10$ and $n(1-p)\ge10$?

Question 5

For $X\sim\mathrm{Binomial}(50,0.5)$, approximate $P(X=25)$ using a normal approximation with continuity correction.