Question

Given a population with a normal distribution, a mean of 12.6 and a standard deviation of 5.35,

A.) what is the probability that a random sample of 10 will have a mean either below 9 or above 10?

B.) if you took a random sample of 12 from this population, how many observations would you expect to be above 13?

Answer 1

Given that, mean (μ) = 12.6 and

standard deviation = 5.35

A) sample size (n) = 10

We want to find the probability that a random sample of 10 will have a mean either below 9 or above 10.

That is to find,

Therefore, required probability is 0.9548

B) Given that, sample size = 12

We want to find, P(X > 13)

Therefore expected number of observations above 13 is,

12 * 0.4721 = 5.6652 ≈ 6

Hence, you would expect approximately 6 observations to be above 13.