Answer to Question #119233 in Statistics and Probability for Prob

Question

5. A recent study shows that the annual cost of maintaining a building in Accra averages
$200 with a variance of $260. If a tax of 30% is introduced on all items associated with the maintenance of building i.e. everything is made 30% more expensive. Calculate the variance of the annual cost of maintaining a building in Accra.

6. Suppose that an airline accepted 12 reservations for a commuter plane with 10 seats.
They know that 7 reservations went to regular commuters who will show up for sure. The other 5 passengers will show up with a 50% chance, independently of each other.
Find the probability that the flight will be overbooked.

7. Suppose that 3% of computer chips produced by a certain machine are defective. The
chips are put into packages of 20 chips for distribution to retailers. What is the probability that a randomly selected package of chips will contain at least 2 defective
chips.

Answer 1

5) Let X represents the annual cost of maintaining a building in Accra, then, E(x)=200, V(x)=260,Let Y represents the annual cost of maintaining a building in Accra after adding a tax of 30%,Y=1.3X

V(Y)=V(1.3X)=1.3²V(x)=1.3²(260)=439.4

6) Find the probability that the flight will be overbooked.

P(X=4)+P(X=5)= C_5,4(0.5)⁴(1−0.5)⁵⁻⁴+C_5,5(0.5)⁵(1−0.5)⁵⁻⁵=(5+1)(0.5)⁵=0.1875

7) n=20,p=0.03

P(x≥2)=1-P(x=0)-P(x=1)

P(x=0)=C_20,0*0.03⁰*(1-0.03)^20-0=0.5438

P(x=1)=C_20,1*0.03¹*0.97¹⁹=0.3363

P(x≥2)=1-0.5438-0.3363=0.12