Question

A desk manufacturer claims that the average time it takes to assemble a desk is 90 minutes with a standard deviation of 32 minutes. Suppose a random sample of 64 desk buyers is taken and time to assemble recorded. The standard deviation of the sample mean is ______ minutes.

Answer 1

The standard deviation of the sample mean is 4 minutes

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:

The standard deviation of the population is 32.

Sample of 64.

So

`s = (32)/(√(64)) = 4`

The standard deviation of the sample mean is 4 minutes