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

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

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 = (\sigma)/(√(n))`

In this problem, we have that:

`\sigma = 39, n = 36`

`s = (39)/(√(36)) = 6.5`

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