A population has a mean of 200 and a standard deviation of 50. Suppose a sample

Question

A population has a mean of 200 and a standard deviation of 50. Suppose a sample size of 100 is selected out of population size of 10,000 and sample mean is used to estimate population mean. What is the probability that the sample mean will be within ±5 of the population mean? A population has a mean of 200 and a standard deviation of 50. Suppose a sample size of 100 is selected out of population size of 10,000 and sample mean is used to estimate population mean. What is the probability that the sample mean will be within ±5 of the population mean? A population has a mean of 200 and a standard deviation of 50. Suppose a sample size of 100 is selected out of population size of 10,000 and sample mean is used to estimate population mean. What is the probability that the sample mean will be within ±5 of the population mean? A population has a mean of 200 and a standard deviation of 50. Suppose a sample size of 100 is selected out of population size of 10,000 and sample mean is used to estimate population mean. What is the probability that the sample mean will be within ±5 of the population mean? A population has a mean of 200 and a standard deviation of 50. Suppose a sample size of 100 is selected out of population size of 10,000 and sample mean is used to estimate population mean. What is the probability that the sample mean will be within ±5 of the population mean? A population has a mean of 200 and a standard deviation of 50. Suppose a sample size of 100 is selected out of population size of 10,000 and sample mean is used to estimate population mean. What is the probability that the sample mean will be within ±5 of the population mean?

Explanation / Answer

Mean is 200 and s is 50, Standard error, SE for 100 sample size is s/sqrt(N)=50/sqrt(100)=5

P(195<x<205)=P((195-200)/5<z<(205-200)/5)=P(-1<z<1)=P(z<1)-(1-P(z<1))=2*P(z<1)-1=2*0.8413-1=0.6826

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