Question

A manufacturing process produces bags of tortilla chips. The bag weights follow a normal distribution with a mean of 16 oz and a standard deviation of 0.8 oz. How many bags should be randomly selected so that the standard error is equal to 0.1 oz

Answer 1

64 bags should be selected.

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:

`\mu = 16, \sigma = 0.8`

How many bags should be randomly selected so that the standard error is equal to 0.1 oz

This is n when s = 0.1. So

`s = (\sigma)/(√(n))`

`0.1 = (0.8)/(√(n))`

`0.1√(n) = 0.8`

`√(n) = 8`

`(√(n))^(2) = 8^(2)`

`n = 64`

64 bags should be selected.