Disposable household income over all Australia in 2005-06 follows the normal distribution with the mean $640 per week and the standard deviation $160 per week. A simple random sample of this population was taken with a sample size of 400.

a)What are the mean and standard deviation of the sampling distribution of the sample means for such samples of size 400 households?

b)Sketch both the population distribution and the sampling distribution of the sample means

for samples of 400 households on the same axis. Indicate on your sketch the mean and the values on the x-axis.

c)What is the probability of a sample of size n=400 having a sample mean household income of $820 per week or more?

d)If the population distribution was positively skewed, would the probability calculations involving the mean of a sample of 400 households be valid? Please explain!