Answer:
The mean is 95 and the standard deviation is 2
Step-by-step explanation:
Central Limit Theorem
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.
In this question:
Population:
Mean 95, Standard deviation 12
Samples of size 36:
By the Central Limit Theorem,
Mean 95
Standard deviation