1. A real estate agent needs to estimate the average value of a residential property of a given area in a certain city. The agent decides to select a large random sample. (a) The agent selects a...

1. A real estate agent needs to estimate the average value of a residential property of a given area in a certain

city. The agent decides to select a large random sample.

(a) The agent selects a random sample of 225 properties in the area and the sample result shows an average of

$200 thousand with a standard deviation $90 thousand. Find a 90% confidence interval for the real average

value.

(b) One year later, the agent will select a large random sample and estimate the average value again. He is

willing to assume that the standard deviation of property values will remain the same as $90 thousand. He

also wishes to ensure that 95% of the times, the estimated average value will be within $2 thousand of the

real average. What is the minimum sample size required?