Sampling And Sampling Distribution Sample Assignment
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Solution: - The population mean is 37.6, with a population standard deviation of 8.3; that is, μ = 37.6 and σ = 8.3. The sample size is 45, but it is being drawn from a finite population of 350; that is, n = 45 and N = 350. The sample mean under consideration is 40, or x = 40. The following diagram depicts the problem on a normal curve.
Using the z formula with the finite correction factor gives
This z value yields a probability of .4808. Therefore, the probability of getting a sample average age of less than 40 years is .4080 +.5000 = .9808. Had the finite correction factor not been used, the z value would have been 1.94, and the final answer would have been .9738.
Sampling And Sampling Distribution Sample Assignment
Question: - A production company’s 350 hourly employees average 37.6 years of age, with a standard deviation of 8.3 years. If a random sample of 45 hourly employees is taken, what is the probability that the sample will have an average age of less than 40 years?Solution: - The population mean is 37.6, with a population standard deviation of 8.3; that is, μ = 37.6 and σ = 8.3. The sample size is 45, but it is being drawn from a finite population of 350; that is, n = 45 and N = 350. The sample mean under consideration is 40, or x = 40. The following diagram depicts the problem on a normal curve.
Using the z formula with the finite correction factor gives
This z value yields a probability of .4808. Therefore, the probability of getting a sample average age of less than 40 years is .4080 +.5000 = .9808. Had the finite correction factor not been used, the z value would have been 1.94, and the final answer would have been .9738.
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