A report announced that the median sales price of new houses

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 $100,000. 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) a.)The sampling distribution will depend on the specific sample and will not have a constant shape.

b.) The sampling distribution will be approximately uniform.

c.)The sampling distribution is skewed to the right, but less skewed to the right than the population.

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 correct answer below)

a.)The sampling distribution will be approximately normal.

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.) The sampling distribution is skewed to the right but lessed skew to the right than the population. If you select a random sample of n =100, what is the probability that the sample mean will be less than $300,000? 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?

Solution

a)

since the size of the sample is small much less than 30 , so, the shape of the distribution is skewed to right

hence C is the correct choice

b)

since the size of the sample much greater than 30 , by central limit theorem, the sampling distribution is approximately normal

hence A is the correct choice

c)

for normal distribution

P(X<x) =P(Z< x-mean/std/sqrt(n))

P(X<300000) = P(Z< ( 300000 - 272200/100000/sqrt(100))

= P(Z<2.78)

= 0.9973

d)

P(280000 <X < 295000) = P(X < 295000) - P( X < 280000)

= P( Z < (295000-272200)/10000) - P(Z<(280000 -272200/10000)

= P(Z < 2.28) - P(Z < 0.78)

= 0.9887 - 0.7823

= 0.2064