C. A contractor has concluded from his experience that the cost of building a lu

Question

C. A contractor has concluded from his experience that the cost of building a luxury home is a normally distributed random variable with a mean of $500,000 and a standard deviation of $40,000.

a. What is the probability that the cost of building a home will be between $380,000 and $550,000?

b. The probability is 0.7 that the cost of the building will be less than what amount?

c. The contractor is bidding on a contract to build a luxury home. He wants to present a range of costs such that he is 80% sure the true cost of building the home will be within this range. What is the shortest range of costs that he might bid?

Explanation / Answer

Ans:

We know that

z = (x-Mean)/sd
x = Mean + (z*sd)

a) z1 = (380000 - 500000)/40000 = - 3
z2 = (550000 - 500000)/40000 = 1.25
The area under the standard normal curve between these two z values indicates the required probability.
Required probability = P(380000 < x < 550000)
= P(- 3 < z < 1.25)
= P(z < 1.25) - P(z < -3)
= 0.89435-0.00135
= 0.893

b)
The z value which separates the lower 0.7 area from the rest (0.3 area) :

z=normsinv(0.7)=0.5244
Required required amount of cost = X = 500000+0.5244*40000
=520976

c) Mean +/- 1.282*sd covers 80% of the values and is represented by 0.8 middle area under the standard normal curve
Therefore, Required range is :

=(Mean-1.282*sd ,Mean + 1.282*sd )
=(500000 - 1.282*40000 , 500000 + 1.282*40000)
=(448720 , 551280)

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.