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# Suppose a large shipment of cell phones contain 21% defective. If the sample of size 204 is selected, what is the probability that the sample proportion will differ from the population proportion by less than 4% round your answer to four decimal places

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## Answer to a math question Suppose a large shipment of cell phones contain 21% defective. If the sample of size 204 is selected, what is the probability that the sample proportion will differ from the population proportion by less than 4% round your answer to four decimal places

Cristian
4.7
The mean of the sampling distribution of the proportion is equal to the population proportion $p$. So, μ = p = 0.21. The standard deviation of the sampling distribution of the proportion $σp̂$ is given by the formula: σp̂ = sqrt [ p$1 - p$ / n ] σp̂ = sqrt [ 0.21 * $1 - 0.21$ / 204 ] ≈ 0.0285 z = $0.04 - 0$ / 0.027 ≈ 1.40265 Using a standard normal distribution table, we find that the probability of a z-score being less than 1.40265 is approximately 0.91964 P = 1 - 2 * $1 - 0.91964$ = 0.83928 So, the probability that the sample proportion will differ from the population proportion by less than 4% is approximately 0.8393 or 83.93% when rounded to four decimal places.
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