The housing market has recovered slowly from the economic crisisof 2008. Recently, in one large community, realtors randomlysampled 30 bids from potential buyers to estimate the average lossin home value. The sample showed the average loss was $9008 with astandard deviation of $1909. Complete parts (a) through (c)below.

a) What assumptions and conditions must be checked beforefinding a confidence interval? How would one check them?

A. The data are assumed to be dependent and to have a samplesize that is large enough to have a sampling distribution that isapproximately Normal. Check the independence assumption by ensuringthat there are at least 10​ \"successes\" and 10​ \"failures.\"

B. The data are assumed to be independent and from a Normalpopulation. Check the independence assumption with the NearlyNormal Condition using a histogram. Check the Normal populationassumption with the Randomization Condition.

C. The data are assumed to be independent and to have a samplesize that is large enough to have a sampling distribution that isapproximately Normal. Check the independence assumption with theRandomization Condition. Check the sample size assumption byensuring that there are at least 10​ \"successes\" and 10​\"failures.\"

D. The data are assumed to be independent and from a Normalpopulation. Check the independence assumption with theRandomization Condition. Check the Normal population assumptionwith the Nearly Normal Condition using a histogram.

b) Find a 90% confidence interval for the mean loss in value perhome.

($___, $___)

(Round to the nearest whole number as needed.)

c) Interpret this interval and explain what 90% confidence meansin this context. Choose the correct answer below.

A. One is 90​% confident that the true average loss in homevalue is between the lower boundary of the interval and the upperboundary of the interval.

B. There is a 90​% chance that the average true loss in homevalue is between the lower boundary of the interval and the upperboundary of the interval.

C. There is a 90​% chance that the true average loss in homevalue of the homes sampled is between the lower boundary of theinterval and the upper boundary of the interval.

D. One is 90​% confident that the true average loss in homevalue of the homes sampled is between the lower boundary of theinterval and the upper boundary of the interval.