Problem 1
Wile E. Coyote loves his ACME Corporation gadgets. The ACME Co. dynamite sticks
Mr. Coyote recently purchased included a timed fuse that was rated for 10 seconds of
burn. Unbeknownst to Mr. Coyote, the fuse burn time follows a normal distribution with
a mean of 10 seconds and a standard deviation of 5 seconds.
a.
Wile E. Coyote has allowed 4.5 seconds for his escape after lighting the fuse.
What is the probability that things will end badly on account of the fuse burn
time?
b.
Mr. Coyote sneaks away from the lit fuse at 1 m/s. What is the mean distance
he will reach before the dynamite explodes?
c.
Following complaints about their low grade fuses, ACME co. switches to a
different fuse style with a uniform distribution between 3 and 8 seconds of
burn time. Will this improve Wile E. Coyote’s escape probability or mean
distance reached?
a.
From the Gaussian distribution
ݐ
̅
ൌ 10, ߪ
௧
ൌ5
ܲሾܾܽ݀ ݐ݄݅݊݃ݏሿൌܲሾݐ൏4
.5ሿ
ݖ
ொ
ൌ
ଵିସ.ହ
ହ
ൌ1
.1
ܲሾݐ൏4
.5ሿ ൌ
ଵ
ଶ
െ
ଵ
ଶ
ܲൣݖ
ொ
൧ൌ
ଵ
ଶ
െ
ଵ
ଶ
∙ 0.7287 ൌ 0.1357
b.
Using expected value of the calculated quantity,
ܧሾݔሿൌܧሾݒ∙ݐሿൌݒ∙ܧሾݐሿൌ1
௦
∙ 10ݏ
ߤ
௫
ൌ 10 ݉
c.
For the uniform distribution,
.5ሿ ൌ
ሺݐሻ݀ݐ
ସ.ହ
ିஶ
ൌ
ଵ
ହ
݀ݐ
ସ.ହ
ଷ
ൌ
ଵ
ହ
ሺ4.5 െ 3ሻ ൌ 0.3000
No, this does not improve his escape probability.
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 Fall '07
 MERKLE
 Normal Distribution, Standard Deviation, Acme Co., Wile E. Coyote, a. Wile E. Coyote

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