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In: Statistics and Probability

Housing prices in Athens have been researched extensively by faculty at UGA. The current thinking is...

Housing prices in Athens have been researched extensively by faculty at UGA. The current thinking is that housing prices follow an approximately normal model with mean $186,000 and standard deviation $7,959. (a) What proportion of housing prices in Athens are less than $176,000? (3 decimal places) (b) A realtor takes a random sample of 123 houses in Athens. Determine the probability the average selling price is greater than $187,000? (3 decimal places) (c) A realtor in Asheville, NC wants to estimate the mean housing price of houses in Asheville. The realtor believes the distribution of housing prices in Asheville is similar to those in Athens. If this realtor takes a random sample of 123 homes in Asheville, what is the standard error of the estimate? (3 decimal places) How many homes in Asheville should the realtor sample to be 98% confident the estimate is within $500 of the true mean price? Use the critical value to exactly 3 decimal places.

Solutions

Expert Solution

a)

Answer:

Proportion = 0.104

Explanation:

Let the random variable, X = housing prices in Athens

The random variable X follows an approximately normal model with mean $186,000 and standard deviation $7,959

The probability is obtained by calculating the z score,

The probability for the z score is obtained from the z distribution table,

b)

Answer:

Probability = 0.082

Explanation:

According to the central limit theorem, the sampling distribution of the sample follows a normal distribution with

The probability is obtained by calculating the z score,

The probability for the z score is obtained from the z distribution table,

c)

Answer:

Sample size = 45

Explanation:

The sample size is obtained using the formula,

Given:

The sample size is,

orchestra answered 2 years ago
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