Answer:
The sampling distribution of the sample mean for samples of size 49 is approximately normally distributed with mean of 100 and standard deviation of 3.
Step-by-step explanation:
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean and standard deviation
, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
and standard deviation
.
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Population
Mean 100, standard deviation 21.
The sampling distribution of the sample mean for samples of size 49
By the Central Limit Theorem
Mean 100
Standard deviation
The sampling distribution of the sample mean for samples of size 49 is approximately normally distributed with mean of 100 and standard deviation of 3.