A report announce the median sales price of new houses sold one year was $221,00

Question

A report announce the median sales price of new houses sold one year was $221,000, and the main sales price was $273,700. Assume that the standard deviation of the prices and his $80,000.
A. If you select samples of n=2, describe the shape of the sampling distribution of x.
B.bIf you select samples of n=100, describe the shape of the sampling distribution of x.
C. If you select a random sample of an equals 100, what is the probability that the sample mean will be less than 300,000? Round to 4 decimals places.
D. If you select a random sample of an pools 100, what is the probability that the sample mean will be between 275,000 and 285,000? Round to four decimal places A report announce the median sales price of new houses sold one year was $221,000, and the main sales price was $273,700. Assume that the standard deviation of the prices and his $80,000.
A. If you select samples of n=2, describe the shape of the sampling distribution of x.
B.bIf you select samples of n=100, describe the shape of the sampling distribution of x.
C. If you select a random sample of an equals 100, what is the probability that the sample mean will be less than 300,000? Round to 4 decimals places.
D. If you select a random sample of an pools 100, what is the probability that the sample mean will be between 275,000 and 285,000? Round to four decimal places
A. If you select samples of n=2, describe the shape of the sampling distribution of x.
B.bIf you select samples of n=100, describe the shape of the sampling distribution of x.
C. If you select a random sample of an equals 100, what is the probability that the sample mean will be less than 300,000? Round to 4 decimals places.
D. If you select a random sample of an pools 100, what is the probability that the sample mean will be between 275,000 and 285,000? Round to four decimal places

Explanation / Answer

A) Since the samples with sample sizes of n=2 is fairly extremely small

a.)The sampling distribution will depend on the specific sample and will not have a constant shape.

B) Since sample size > 30 as per the central limit theorem

a.)The sampling distribution will be approximately normal.

C)
P(X < 300000) = (300000-273700)/80000/ Sqrt ( 100 )
= 26300/8000= 3.2875
= P ( Z <3.2875) From Standard NOrmal Table
= 0.9995                  
D)
To find P(a <= Z <=b) = F(b) - F(a)
P(X < 275000) = (275000-273700)/80000/ Sqrt ( 100 )
= 1300/8000
= 0.1625
= P ( Z <0.1625) From Standard Normal Table
= 0.56454
P(X < 285000) = (285000-273700)/80000/ Sqrt ( 100 )
= 11300/8000 = 1.4125
= P ( Z <1.4125) From Standard Normal Table
= 0.9211
P(275000 < X < 285000) = 0.9211-0.56454 = 0.3566

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