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Test by Bikram | Mock GATE | Test 3 | Question: 49

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In a hospital $’X’$ births occur randomly at an average rate of $1.8$ births per hour.

The probability that we observe $5$ births in a given interval of $2$ hours is ______.
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This problem is based on Poisson Distribution 

1.8 births per 1 hour interval then 3.6 births per 2 hour interval .

P(X = 5) = e-3.6 ( 3.65/ 5! ) 

= 0.0273 ( 604.66 / 120) 

=  0.0273 *  5.0388

= 0.13756

Reference:

http://www.stats.ox.ac.uk/~marchini/teaching/L5/L5.slides.pdf

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unfortunately i got 0.1376
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