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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

1 Answer

4 votes

Answer:

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.

User Calin Chitu
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