Question

Random samples of size 36 each are taken from a large population whose mean is 120 and standard deviation is 39. The standard error of the sampling distribution of sample mean is:_______

Answer 1

Answer:

The standard error of the sampling distribution of sample mean is: 6.5

Step-by-step explanation:

We use the Central limit theorem to solve this question.

The Central Limit Theorem estabilishes that, for a random variable X, with mean $\mu$ and standard deviation $\sigma$, a large sample size can be approximated to a normal distribution with mean $\mu$ and standard deviation, which is also called standard error of the sampling distribution of sample mean is $s = \frac{\sigma}{\sqrt{n}}$

In this problem, we have that:

$\sigma = 39, n = 36$

$s = \frac{39}{\sqrt{36}} = 6.5$

The standard error of the sampling distribution of sample mean is: 6.5