Answer:
represent the sample mean
represent the sample deviation
n = 68 represent the sample size
Since the sample size is large enough n>30 we have enough evidence to conclude that the normal approximation for the sample mean makes sense. And the distribution for the sample mean would be given by:
Explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".
Solution to the problem
For this case we have the following data given:
represent the sample mean
represent the sample deviation
n = 68 represent the sample size
Since the sample size is large enough n>30 we have enough evidence to conclude that the normal approximation for the sample mean makes sense. And the distribution for the sample mean would be given by: