3. Probability Distributions

Normal Approximation — Quiz

Test your understanding of normal approximation with 5 practice questions.

Practice Questions

Question 1

A population has a mean of $ \mu = 70 $ and a standard deviation of $ \sigma = 10 $. If a random sample of $ n = 100 $ is taken, what is the probability that the sample mean ($ \bar{x} $) is between 68.5 and 71.5?

Question 2

A binomial distribution has $ n = 200 $ trials and a probability of success $ p = 0.6 $. What is the probability that the number of successes ($ X $) is exactly 125, using the normal approximation with continuity correction?

Question 3

A random variable $ X $ follows a Poisson distribution with a mean of $ \lambda = 49 $. What is the probability that $ X $ is less than 45, using the normal approximation with continuity correction?

Question 4

A manufacturing process produces items with a defect rate of 5%. If a random sample of 500 items is inspected, what is the approximate probability that the number of defective items is between 20 and 30 (inclusive), using the normal approximation?

Question 5

A random variable $ X $ represents the number of calls received by a call center in an hour, following a Poisson distribution with a mean of $ \lambda = 64 $. What is the probability that the call center receives more than 70 calls in an hour, using the normal approximation with continuity correction?