Question

The operating costs for each machine for one day have an unknown distribution with mean 1610 and standard deviation 136 dollars. A sample, with size n=45, was randomly drawn from the population. Using the Central Limit Theorem for Means, what is the standard deviation for the sample mean distribution? Select the correct answer below: 3.02 20.27 25.34 30.41 34.47 136.00

Answer 1

Answer:

20.27

Step-by-step explanation:

The Central Limit Theorem estabilishes that, for a random variable X, with mean $\mu$ and standard deviation $\sigma$, the sample means with size n of at least 30 can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$

Using the Central Limit Theorem for Means, what is the standard deviation for the sample mean distribution?

This is s when $\sigma = 136, n = 45$. So

$s = \frac{136}{\sqrt{45}} = 20.27$

So the correct answer is:

20.27