# another S2 questionWatch

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#1
street light failtures in a town occur at an average rate of one every two days. Assusing that X, the number of street light failures per week, has a poisson distrubition, find to 3 dp using the tables provided or otherwise, the probabilities that the number of street lights will fail in a given week is

a) excatly 2
b)less that 6

c) using an approx distribution that approxiamates to that of x, find to 3 dp the probabilty that there will be fewer than 45 street light failures in 10 weeks
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14 years ago
#2
Let X be r.v. # of street lights failing per week
------------
X~Po(3.5)

P(X = 2) = P(X <= 2) - P(X <= 1)
= 0.3208-0.1359
= 0.1849
= 0.185 (3 dp)
---------

P(X < 6) = P(X <= 5)
= 0.8576
= 0.858 (3 dp)
---------
Let Y be r.v. # of failures in 10 week period

Y~Po(3.5 * 10)
so: Y~Po(35)

as > 10 use normal distribution to approximate

with µ = σ = λ = 35

so:

P(X < 45) = P(Y < 44.5) (---Half continuity correction - discret -> continious)
= P(z < (44.5 - 35)/√35)
= P(z < 1.61)
= ф(1.61)
= 0.9463
= 0.946 (3dp)

Think that should be right

MdSalih
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