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The mayor of a large city would like to portray the city as place with affordable housing. City officials take a sample of 133 houses and find an average selling price of $173,000 with a standard deviation of $6,714.

(a) What is the standard error of the average house price for a sample of 133 houses?  (Use 4 decimals.)

(b) A certain family moving into this area budgeted $164,000 for a house. For this particular neighborhood, housing prices are roughly symmetric and unimodal. What is the probability they can actually find a house in this city for less than $164,000?  (Use 4 decimals.)

(c) If the mayor's office takes another sample of 133 houses, what is the probability this sample will show an average house price greater than $174,000? (Use 4 decimals.)

(d) The mayor's office would like to have a precise estimate of the mean selling price. How many houses in the city need to be sampled to be 98% confident the average selling price is within $500 of the true mean price?

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