Question

3. The mean family income in Arizona is about $64,750 with a standard deviation (for the population) of $59,750. Imagine that you are taking a sample of 200 randomly selected state residents. (a) What is the probability that your sample mean is between $61,000 and $64,750? (b) For this same sample size, what is the probability that the sample mean exceeds $75,000? (c) What income levels would correspond with the 95% confidence limits for this sample? (d) Interpret what these 95% confidence limits tell us

Answer 1

Since you are dealing with a distribution of means rather than raw scores, use the following equation and the same table.

Z = (score-mean)/SEm

SEm = SD/√n

95% = mean ± 1.96 SEm

Answer 2

31.59%