Data from the Bureau of Labor Statistics’ Consumer Expenditure Survey (CE) show

Question

Data from the Bureau of Labor Statistics’ Consumer Expenditure Survey (CE) show that annual expenditures for cellular phone services per consumer unit increased from $259 in 2001 to $603 in 2007. Let the standard deviation of annual cellular expenditure be $69 in 2001 and $166 in 2007. Use Table 1.

What is the probability that the average annual expenditure of 121 cellular customers in 2001 exceeded $242? (Round “z” value to 2 decimal places, and final answer to 4 decimal places.)

What is the probability that the average annual expenditure of 121 cellular customers in 2007 exceeded $611? (Round “z” value to 2 decimal places, and final answer to 4 decimal places.)

What is the probability that the average annual expenditure of 121 cellular customers in 2001 exceeded $242? (Round “z” value to 2 decimal places, and final answer to 4 decimal places.)

Explanation / Answer

a) for this mean = 259

standard dev = 69

For x = 242, z = (242 - 259) / 69 = 0.24

Hence P(x > 242) = P(z > 0.24) = [total area] - [area to the left of 0.24]

= 1 - 0.5948 = 0.4052

b) mean = 603

standard dev = 166

p(x>611) =

For x = 611, z = (611 - 603) / 166 = 0.04

Hence P(x > 611) = P(z > 0.04) = [total area] - [area to the left of 0.04]

= 1 - 0.5160 = 0.0.4840

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