Question

# A gigantic warehouse stores approximately 40 million empty aluminum beer and soda cans.​ Recently, a fire...

A gigantic warehouse stores approximately 40 million empty aluminum beer and soda cans.​ Recently, a fire occurred at the warehouse. The smoke from the fire contaminated many of the cans with​ blackspot, rendering them unusable. A statistician was hired by the insurance company to estimate​ p, the true proportion of cans in the warehouse that were contaminated by the fire. How many aluminum cans should be randomly sampled to estimate p to within 0.08 with 90​% confidence?

The margin of error we desire is ME = 0.08, and for 90% confidence, we use Z0.05= 1.645 (well-known value using Z table).

Since we have no prior knowledge about the proportion p, we use the conservative estimate of = 0.5.

We have:

So, n =106 aluminum cans should be randomly sampled to estimate p to within 0.08 with 90​% confidence.

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