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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.

Other Sample Assignments in Statistics Homework Assignment :

Continious Distribution	Descrete Distributions
Descriptive Statistics	Nonparamatric Statistics
Probability	Sampling And Sampling Distribution
Statistical Inference Estimation For Single Popula	Simple Regression Analysis
Statistical Inference About 2 Population	Time Series Forcasting Index Number
Statistical Quality Control	Correlation
Index Number	Larger Sample Mean Proportions
Non Parametric Test	Probability Theory
Sampling Distribution	Simple and Multiple Linear Regression Analysis
Unvariate Analysis

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