Question

A report announced that the median sales price of new houses sold one year was ?$211,000?, and the mean sales price was ?$274,200. Assume that the standard deviation of the prices is ?$90,000. 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 below. A.The sampling distribution is skewed to the? right, but less skewed to the right than the population. B.The sampling distribution will depend on the specific sample and will not have a constant shape. C.The sampling distribution will be approximately uniform. D.The sampling distribution will be approximately normal. (b)If you select samples of n=100?, describe the shape of the sampling distribution of X. Choose the correct answer below. A.The sampling distribution will be approximately uniform. B.The sampling distribution will depend on the specific sample and will not have a constant shape. C.The sampling distribution will be approximately normal. 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 ?$290,000?? The probability that the sample mean will be less than ?$290,000 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 ?$275,000 and ?$285,000?? The probability that the sample mean will be between ?$275,000 and ?$285,000 is ? ?(Round to four decimal places as? needed.)

Answer 1

Ans:

a)The sampling distribution is skewed to the? right, but less skewed to the right than the population.(as population is skewed and sample size is very small)

b)The sampling distribution will be approximately normal.(as sample size is sufficiently large)

c)mean=274200

standard error of mean=90000/sqrt(100)=9000

z=(290000-274200)/9000

z=1.756

P(z<1.756)=0.9604

d)

z(275000)=(275000-274200)/9000=0.089

z(285000)=(285000-274200)/9000=1.2

P(0.089<z<1.2)=0.8849-0.5354=0.3495