The average income in Connecticut in 2013 was $60,000 per person per year. Suppo

Question

The average income in Connecticut in 2013 was $60,000 per person per year. Suppose the the standard deviation is $30,000 and the distribution is right-skewed. Suppose we take a random sample of 400 residents of Connecticut. We want to find the probability that the sample mean will be more than $3000 away from the population mean.

a)Why is the distribution Normal and not right-skewed like the population?

b)Why is the z-score 2?

c)What is the probability that the sample mean will be more than $3000 away from the population mean?

Explanation / Answer

a) According to central limit theorem, if repeated sample size of N are drawn from any population with mean mu and standard deviation sigma, then as N becomes large, th esampling distribution of sample means will approach normality. This tells why the distribution is normal (N=400) and not right skewed.

b. The z score is positive and 2 stndard deviation above the population mean.

c. The area corresponding to z=2 is 0.4772, this gives the required probability.

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