Question

Selling buying a home has become very difficult due to the economical crisis which has severely affected the housing sector in recent years. Home sellers participating in a survey indicated that it typically takes between 6 and 14 months to sell a house. Suppose that the distribution of the time that it takes to sell a house can be approximated by a normal distributed with a mean of 10 months and a population standard deviation of 3 months.

(a) What percent of the homes take less than 9 months to sell?

(b) What percent of the homes take between 10 and 16 months to sell?

(c) How long does it take for top 10% of the houses to be sold?

(d) If 25 sold homes were randomly selected, what is the probability that the sample mean is less than 9 months? Hint: Use central limit theorem.

(e) Which one is more likely to happen: Randomly selecting a home that takes less than 9 months to sell (part-a) or Finding a random sample of 25 homes with a mean selling time of less than 9 months (part-d). Compare parts a and d, and enter a or d in the box below.

Answer 1

a)

for normal distribution z score =(X-μ)/σ
here mean=       μ=	10
std deviation   =σ=	3.0000

probability =

P(X<9)

=

P(Z<-0.33)=

0.3707~37.07%

b)

probability =

P(10<X<16)

=

P(0<Z<2)=

0.9772-0.5=

0.4772~47.72%

c)

for 90th percentile critical value of z=		1.28
therefore corresponding value=mean+z*std deviation=			13.84 months

d)

sample size       =n=	25
std error=σx̅=σ/√n=	0.6000

probability =

P(X<9)

=

P(Z<-1.67)=

0.0475~ 4.75%

e)

option A is correct