Question

1)Flying over the western states with mountainous terrain in a small aircraft is 40% riskier than flying over similar distances in flatter portions of the nation, according to a General Accounting Office study completed in response to a congressional request. The accident rate for small aircraft in the 11 mountainous western states is 2.5 accidents per 100,000 flight operations.  Find the probability of at least 6 accidents in 208,000 flight operations. (Use 4 decimal places.)

2) Consumer Banker Association released a report showing the lengths of automobile leases for new automobiles. The results are as follows.

Lease Length in Months	Percent of Leases
13-24 25-36 37-48 49-60 More than 60	12.4% 37.6% 25.0% 24.6% 0.4%

Use the midpoint of each class, and call the midpoint of the last class 66.5 months, for purposes of computing the expected lease term. Also find the standard deviation of the distribution. (Round your answers to two decimal places.) a) expected lease term in months b) standard deviation

3)In Hawaii, the rate of motor vehicle theft is 775 thefts per 100,000 vehicles. A large parking structure in Honolulu has issued 589 parking permits. (a) What is the probability that none of the vehicles with a permit will eventually be stolen? (Round λ to 1 decimal place. Use 4 decimal places for your answer.) (b) What is the probability that nine or more vehicles with a permit will eventually be stolen? (Use 4 decimal places.)

Answer 1

1)expected accidents in 208,000 flight operations =2.5*208000/100000=5.2

hence

probability of at least 6 accidents in 208,000 flight operations =P(X>=6)=1-P(X<=5)=0.4191

x	P(x)	xP(x)	x2P(x)
18.5	0.124	2.294	42.439
30.5	0.376	11.468	349.774
42.5	0.25	10.625	451.563
54.5	0.246	13.407	730.682
66.5	0.004	0.266	17.689
	total	38.060	1592.146
	E(x) =μ=	ΣxP(x) =	38.0600
	E(x2) =	Σx2P(x) =	1592.1460
	Var(x)=σ2 =	E(x2)-(E(x))2=	143.582
	std deviation=	σ= √σ2 =	11.9826

a)

expected lease term =38.06

b) standard deviation =11.9826

3)

\ λ =(775*589/100000)=4.6

probability that none of the vehicles with a permit will eventually be stolen =e^-4.6*4.6⁰/0! =0.0101

b) probability that nine or more vehicles with a permit will eventually be stolen =0.0451