Suppose the population mean μ=50 and standard deviation σ=5. If you select a random sample of 49 observations, What is the probability that the sample average, X ̅, is greater than 47.7?
+33653 Standard error on the mean is standard deviation/sqrt(sample size) = 5/7 ≈ 0.714
Number of standard errors between 50 and 47.7 = (50 - 47.7)/0.714 ≈ 3.22
Probability of being more than 3.22 standard errors away from the mean on a normal distribution ≈ 0.0007
Hence probability sample average is greater than 47.7 is ≈ 0.9993
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