Homework #6-Chapter 5&11 (20pts for turned in on time) 11. (10pts)The idea of in

Question

Homework #6-Chapter 5&11 (20pts for turned in on time) 11. (10pts)The idea of insurance is that we al face risks that are unlikely but carry high cost. Think of a fire destroying your home. So we form a group to share the risk:We al pay a smalil amount, and the insurance policy pays a large amount to those few of us whose homes burnt down. The loss from fire for home owners is extremely right skewed, since most of the home owners don't lose at all, but a few of them whose house is burnt will lose between hundreds of thousand dollars each. A research was done and found out that the average loss due to fire is $250, and the standard deviation is $1000 across United States. Use Central Limit Theorem to answer the questions below: (1) (4pts)A small local insurance company only has 100 customers. What is the chance that the average home loss due to fire raise to $300 or higher? (2) (4pts)A national big insurance company has 10,000 customers. What is the chance that the average home loss due to fire raise to $300 or higher?

Explanation / Answer

1) P(X > 300)

= P((X - mean)/(sd/sqrt(n)) > (300 - mean)/(sd/sqrt(n)))

= P(Z > (300 - 250)/(1000/sqrt(100)))

= P(Z > 0.5)

= 1 - P(Z < 0.5)

= 1 - 0.6915

= 0.3085

b) P(X > 300)

= P((X - mean)/(sd/sqrt(n)) > (300 - mean)/(sd/sqrt(n)))

= P(Z > (300 - 250)/(1000/sqrt(10000)))

= P(Z > 5)

= 1 - P(Z < 5)

= 1 - 1 = 0

Related Questions

Navigate

• Browse (All)
• Browse H
• Subjects

---

---

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