Question

Suppose that a population is known to be normally distributed with

μ =2,300 and σ=250. If a random sample of size

n =8 is​ selected, calculate the probability that the sample mean will exceed

2,400.

Answer 1

According to the central limit theorem, the distribution of sample mean here is given as:

Note that even if the sample size is small, the central limit theorem is applicable as the underlying distribution is normal distribution.

Converting it to a standard normal variable, we get:

Getting it from the standard normal tables, we get:

Therefore 0.1289 is the required probability here.