Answer:
The standard deviation of the sampling distribution of the sample mean score for a random sample of 36 students is 1.
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.
In this problem, we have that:
![\sigma = 6, n = 36](https://tex.z-dn.net/?f=%5Csigma%20%3D%206%2C%20n%20%3D%2036)
Then, by the Central Limit Theorem:
![s = \frac{\sigma}{\sqrt{n}}](https://tex.z-dn.net/?f=s%20%3D%20%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D)
![s = \frac{6}{\sqrt{36}}](https://tex.z-dn.net/?f=s%20%3D%20%5Cfrac%7B6%7D%7B%5Csqrt%7B36%7D%7D)
![s = 1](https://tex.z-dn.net/?f=s%20%3D%201)
The standard deviation of the sampling distribution of the sample mean score for a random sample of 36 students is 1.