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

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Cristian

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71 Answers

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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