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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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he 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 two accidents will occur on this stretch of road during a randomly selected month.
Solution:
P(x < 2) = P(x = 0) + P(x = 1)
Ans: 0.000860
X not X N(X) P(X) X*P(X) Σ (N) Σ (P)
----- ----- ------------ ------------- -------------- ------------- --------------
1 4 8 1/99 0.0101 8 0.010101010101
2 3 112 14/99 0.2828 120 0.151515151515
3 2 336 14/33 1.2727 456 0.575757575757
4 1 280 35/99 1.4141 736 0.929292929292
5 0 56 7/99 0.3535 792 1
------------ ------------- -------------- ------------- --------------
totals: 792 1 3.3333
Answer: 14/33
Solution:
a)
The Poisson distribution is,
P(x=x) =e-xx/x! (x=0, 1, 2, 3…)
Here =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 Solution:- b) The hyper 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) =? =8c3 4c2/12c5 = 56*6/792 = 336/792 =0.4242
Thanks dosary ka b solution du
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