Question

In a sample of 115 115 curtains, the average length was found to be 32.2in. 32.2 ⁢ in. With a standard deviation of 0.8 0.8 . Give a point estimate for the population standard deviation of the length of the curtains. Round your answer to two decimal places, if necessary.

Answer 1

Answer:

The point estimate for the population standard deviation of the length of the curtains is 8.58in.

Step-by-step explanation:

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

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:

$s = 0.8, n = 115$

The point estimate for the population standard deviation of the length of the curtains is $\sigma$. So

$s = \frac{\sigma}{\sqrt{n}}$

$\sigma = s\sqrt{n}$

$\sigma = 0.8\sqrt{115}$

$\sigma = 8.58$

The point estimate for the population standard deviation of the length of the curtains is 8.58in.