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(a) The number of traffic accidents that occurs on a particular stretch of road during a month follows a Poisson distribution with a mean of 9.4. Find the probability that less than four accidents will occur on this stretch of road during a randomly selected month.

(b) Twelve people apply for a job as Lecturer in a College. Eight have completed graduation and four have not. If the Principal selects five applications at random, find the probability that three are graduate and two are not.

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Complete solution

STA 301                     GDB 3

 

Solution:

 a)

The Poisson distribution is

P(x=x) =e-xmx/x!                     (x=0, 1, 2, 3…)

Here    m=9.4

P(x<4) =?

P(x<4) =P(x=0) +P(x=1) +P(x=2) +P(x=3)

P(x<4) =0.000083+0.00078+0.0037+0.0115

P(x, 4) =0.01606

b)    

Thehyper geometric p.d is

P(x=x) =kcxN-kcn-x/Ncn

Here

N=12                       k=8           n=5

P(x=3 are graduate & two are not) =?

         =8c34c2/12c5

  = 56*6/792

         = 336/792

 =0.4242               

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