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

Answer:

64 bags should be selected.

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:

$\mu = 16, \sigma = 0.8$

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

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

$0.1 = \frac{0.8}{\sqrt{n}}$

$0.1\sqrt{n} = 0.8$

$\sqrt{n} = 8$

$(\sqrt{n})^{2} = 8^{2}$

$n = 64$

64 bags should be selected.