Suppose a subdivision on the southwest side of Denver, Colorado, contains 1,500 houses. The subdivision was built in 1983. A sample of 120 houses is selected randomly and evaluated by an appraiser. If the mean appraised value of a house in this subdivision for all houses is $229,000, with a standard deviation of $8,700, what is the probability that the sample average is greater than $230,500? Appendix A Statistical Tables. (Round the values of z to 2 decimal places. Round your answer to 4 decimal places.)
Solution :
_{} = / n = 8700 / 120 = 794.1977
P( > 230500) = 1 - P( < 230500)
= 1 - P[( - _{} ) / _{} < (230500 - 229000) / 794.1977]
= 1 - P(z < 1.89)
= 1 - 0.9706
= 0.0294
Probability = 0.0294
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