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 statistician should sample nothing cans to estimate the proportion that were contaminated by the fire to within 0.08 with 90% confidence. (Round up to the nearest can.)

106

Step-by-step explanation:

Let p be the true population proportion of cans in the warehouse that were contaminated by the fire.

The formula to find the required sample size when the prior populatio proportion is unknown:

, where z* = Critical z-value related to confidence interval and E = Margin of error.

As per given , we have

E= 0.08

Critical z-value for 90% confidence level = 1.645

Then, substitute all values in formula , we get

Hence, the statistician should sample 106 cans to estimate the proportion that were contaminated by the fire to within 0.08 with 90% confidence.

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