Question

A report announced that the median sales price of new houses sold one year was ​$211,000​, and the mean sales price was ​$271,200. 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 Upper X over bar. Choose the correct answer below. 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 will be approximately normal.

D. The 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 Upper X over bar. Choose the correct answer below.

A. The sampling distribution will be approximately uniform.

B. The sampling distribution is skewed to the​ right, but lessed skew to the right than the population.

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

D. The sampling distribution will be approximately normal. ​

(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 0.9998. ​(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 ​$295,000​? The probability that the sample mean will be be between ​$275,000 and ​$295,000 is ???. ​(Round to four decimal places as​ needed.)

Answer 1

a)

D. The sampling distribution is skewed to the​ right, but less skewed to the right than the population.

b)

D. The sampling distribution will be approximately normal. ​

c)

sample size       =n=	100
std error=σx̅=σ/√n=	8000.0000
probability =	P(X<300000)	=	P(Z<3.6)=	0.9998

d)

probability =

P(275000<X<295000)

=

P(0.48<Z<2.98)=

0.9986-0.6844=

0.3142

(try 0.3159 if this comes wrong and revert)