Answer:
E. Approximately normal with standard deviation less than 0.7 sibling
Step-by-step explanation:
To solve this question, we use the Central Limit theorem.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a random variable X, with mean
and standard deviation
, a large sample size can be approximated to a normal distribution with mean
and standard deviation ![s = \frac{\sigma}{\sqrt{n}}](https://tex.z-dn.net/?f=s%20%3D%20%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D)
In this problem, we have that:
Skewed right distribution, with ![\mu = 1.8, \sigma = 0.7](https://tex.z-dn.net/?f=%5Cmu%20%3D%201.8%2C%20%5Csigma%20%3D%200.7)
Sampling distribution of the sample mean for samples of size 100
By the Central Limit Theorem, they will be approximately normal, with mean
, and standard deviation ![s = \frac{0.7}{\sqrt{100}} = 0.07](https://tex.z-dn.net/?f=s%20%3D%20%5Cfrac%7B0.7%7D%7B%5Csqrt%7B100%7D%7D%20%3D%200.07)
So the correct answer is:
E. Approximately normal with standard deviation less than 0.7 sibling