Answer:
The shape of the distribution of the sample mean would be bell-shaped(normally distributed).
Step-by-step explanation:
The Central Limit Theorem answers this question.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a random variable X, with mean and standard deviation
, a large sample size, of at least 30, can be approximated to a normal distribution with mean
and standard deviation
.
In this problem, we have that
The population distribution is right-skewed.
Sampling distribution of the sample mean with size 40.
The Central Limit Theorem estabilishes that the sampling distribution of the sample mean will be normally distributed, even if the distribution of the population is not.
So the shape of the distribution of the sample mean would be bell-shaped(normally distributed).
