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 ??

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)

for normal distribution z score =(X-μ)/σ
here mean=       μ=	271200
std deviation   =σ=	80000.0000
sample size       =n=	100
std error=σx̅=σ/√n=	8000.0000

probability =

P(X<300000)

=

P(Z<3.6)=

0.9998