A report announced that the median sales price of new houses sold one year was $

Question

A report announced that the median sales price of new houses sold one year was $221,000, and the mean sales price was $272,200. Assume that the standard deviation of the prices is $80,000. Complete parts (a) through (d) below. (a) If you select samples of n 2, describe the shape of the sampling distribution of X. Choose the correct answer belovw A. The sampling distribution will be approximately normal. O B. The sampling distribution will be approximately uniform. C. The sampling distribution will depend on the specific sample and will not have a constant shape D , Then sampling distribution is skewed to the right, but less skewed to the right than the population (b) If you select samples of n = 100, describe the shape of the sampling distribution of X, Choose the correct answer below OA. The sampling distribution will be approximately normal. O B. The sampling distribution will be approximately uniform. ° C. The sampling distribution will depend on the specific sample and will not have a constant shape O D. The sampling distribution is skewed to the right, but lessed skew to the right than the population. (c) If you select a random sample of n 100, what is the probability that the sample mean will be less than $300,000? The probability that the sample mean will be less than $300,000 is . Round to four decimal places as needed.) (d) If you select a random sample of n = 100, what is the probability that the sample mean will be between $280,000 and $295,000?

Explanation / Answer

a)as mean is greater then median

option D is correct

b) option A is correct

c)

here mean =272200

std deviation of sample mean =80000/(100)1/2 =8000

probability =P(X<300000)=P(Z<(300000-272200)/8000)=P(Z<3.475)=0.9997

d) P(280000<X<295000)=P((280000-272200)/8000<Z<(295000-272200)/8000)=P(0.975<Z<2.85)=0.9978-0.8352

=0.1626

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