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Economics 320: Homework 7
Continuous Distributions: Exponential
Sampling Distributions
EXPONENTIAL DISTRIBUTION:
1.
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 claims per month.
a.
What is the probability that the dealership will wait at least 6 months until the
next claim?
i.
λ is the mean number of occurrences per time unit ; so λ = 0.1
ii.
F(x) = 1 
x
e
λ

for x > 0.
iii.
P(x > 6) =
x
e

=
6
*
1
.
0

e
= 0.5488
b.
At least a year?
i.
P(x > 12) =
x
e

=
12
*
1
.
0

e
= 0.3012
c.
At least 6 months but not more than 1 year?
i.
P(6 < x < 12) = (1 
12
*
1
.
0

e
)

(1 
6
*
1
.
0

e
) = 0.2476
2.
In 1982, the inflight shutdown rate for the Garrett TFE731 turbofan engine was 6.0
shutdowns per 100,000 hours.
In 1992, with improvements, the inflight shutdown rate
for this same engine dropped to 1.5 shutdowns per 100,000 hours.
a.
Find the probability that at least 50,000 hours would elapse before the next in
flight shutdown in 1982.
i.
λ is the mean number of occurrences per time unit ; so λ(1982) = 6 and λ(1992) = 1.5
ii.
for 1982: P(x > ½) =
5
.
0
*
6

e
= 0.0498
b.
Calculate the same probability in 1992.
i.
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