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

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

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 = (\sigma)/(√(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 = (\sigma)/(√(n))`

`\sigma = s√(n)`

`\sigma = 0.8√(115)`

`\sigma = 8.58`

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