Automobile warranty claims for engine mount failure in a Troppo Malo 2000 SE are

Question

Automobile warranty claims for engine mount failure in a Troppo Malo 2000 SE are rare at a certain dealership, occurring at a mean rate of 0.1 claim per month.

What is the probability that the dealership will wait at least 6 months until the next claim? (Round your answer to 4 decimal places.)

What is the probability that the dealership will wait at least a year? (Round your answer to 4 decimal places.)

What is the probability that the dealership will wait at least 2 years? (Round your answer to 4 decimal places.)

What is the probability that the dealership will wait at least 6 months but not more than 1 year? (Round your answer to 4 decimal places.)

Automobile warranty claims for engine mount failure in a Troppo Malo 2000 SE are rare at a certain dealership, occurring at a mean rate of 0.1 claim per month.

Explanation / Answer

a.What is the probability that the dealership will wait at least 6 months until the next claim?

i. is the mean number of occurrences per time unit ; so = 0.1

ii.F(x) = 1 -e^x-for x > 0.

iii.P(x > 6) =e^-x=e^-6*1.0= 0.5488

b.At least a year?

.P(x > 12) =e^-x-=e^-12*1.0= 0.3012

c) P(X>=2) = 1-P(X<2) = 1-P(0)+P(1)

=1-e^0.1[1+0.1] = 1-e^0.1*1.1'

= 1-e^0.11 = 1-0.8958=0.1042

d) .At least 6 months but not more than 1 year?

i.P(6 < x < 12) = (1 - e^-12*1.0)-(1 -e^-6*1.0) = 0.2476

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