In the EAI sampling problem, the population mean is $51,900 and the population s

Question

In the EAI sampling problem, the population mean is $51,900 and the population standard deviation is $5,000. When the sample size is n = 30, there is a 0.4176 probability of obtaining a sample mean within +/- $500 of the population mean. What is the probability that the sample mean is within $500 of the population mean if a sample of size 60 is used (to 4 decimals)? What is the probability that the sample mean is within $500 of the population mean if a sample of size 120 is used (to 4 decimals)?

Explanation / Answer

using tables of normla distribution we cna find each probability

. What is the probability that the sample mean is within $500 of the population mean if a sample of size 60 is used (to 4 decimals)?

P( -500 / 5000 / srqt 60 < z < 500 / 5000 / srqt 60 )

P( -0.77 < z < 0.77) = 1 - 0.2206 - 0.2206 = 0.5588

What is the probability that the sample mean is within $500 of the population mean if a sample of size 120 is used (to 4 decimals)?

P( -500 / 5000 / srqt 120 < z < 500 / 5000 / srqt 120 )

P( -1.10 < z < 1.10 ) = 1 - 0.1357 - 0.1357 = 0.7286

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