# Question: For the population of farm workers in New Zealand suppose

For the population of farm workers in New Zealand, suppose that weekly income has a distribution that is skewed to the right with a mean of μ = +500 (N.Z.) and a standard deviation of σ = +160. A researcher, unaware of these values, plans to randomly sample 100 farm workers and use the sample mean annual income x to estimate μ.

a. Show that the standard deviation of x equals 16.0.

b. Explain why it is almost certain that the sample mean will fall within $48 of $500.

c. The sampling distribution of x provides the probability that x falls within a certain distance of μ, regardless of the value of μ. Show how to calculate the probability that x falls within $20 of μ for all such workers. (Using the standard deviation, convert the distance 20 to a z -score for the sampling distribution.)

a. Show that the standard deviation of x equals 16.0.

b. Explain why it is almost certain that the sample mean will fall within $48 of $500.

c. The sampling distribution of x provides the probability that x falls within a certain distance of μ, regardless of the value of μ. Show how to calculate the probability that x falls within $20 of μ for all such workers. (Using the standard deviation, convert the distance 20 to a z -score for the sampling distribution.)

## Answer to relevant Questions

The previous exercise reported that for the population, μ = +500 and σ = +160, and that the sample mean income for a random sample of 100 farm workers would have a standard deviation of 16.0. Sketch the sampling ...According to the 2010 U.S. Census Bureau Current Population Survey (www.census.gov/population/www/socdemo/hh-fam/cps2010.html), the average number of people in family households which contain both family and non-family ...According to the Alzheimer’s Association1, as of 2011 Alzheimer’s disease affects 1 in 8 Americans over the age of 65. A study is planned of health problems faced by the elderly. For a random sample of Americans over the ...The scores on the Psychomotor Development Index (PDI), a scale of infant development, have a normal population distribution with mean 100 and standard deviation 15. An infant is selected at random. a. Find the z -score for a ...As the sample size increases, the standard deviation of the sampling distribution of x increases. Explain your answer.Post your question