Question

1. Aaron Purr, the best cat in the world chases an average of 12 birds per day. He is not a mighty hunter and rarely catches any. But that's ok, we'll use his chasing info for this problem a. What is the probability that, today, Aaron Purr will chase more than 9 birds? p(9 b. What is the probability that Aaron Purr will chase exactly 7 birds within 12 hours tomorrow? І

Answer 1

The number of birds chased per day is modelled here as:

$x \sim Poisson(12)$

a) The probability that Purr will chase more than 9 birds in a day is computed here as:
P(X > 9) = 1 - P(X <= 9)

This is computed in EXCEL as:
=1-poisson.dist(9,12,TRUE)

0.7576 is the output here.

Therefore 0.7576 is the required probability here.

b) For a 12 hour period, that is half day the mean number of birds chased in half a day is computed here as:
= 0.5*12 = 6

Therefore the probability here is computed as:

= P(X = 7)

$= \frac{6^7}{7!}e^{-6} = 0.1377$

Therefore 0.1377 is the required probability here.