Jacob and Ashley run an animal shelter that houses only cats

Jacob and Ashley run an animal shelter that houses only cats and dogs . The ratio of cats to dogs is 5:4. Of the cats 40% are kittens, while 3/7 of the dogs are puppies. The shelter houses a total of 63 animals.

What I know- Total Cats=35 Kittens=14 Adult Cats=21 Total Dogs=28 Puppies=12 Adult Dogs=16

What I ned to know- A group of 10 baby animals is chosen from the shelter. Is the probability distribution for the makeup of this group symmetric or skewed? Justify your answer. Thank You

Solution

Let no of cats = 5x and dogs = 4x

Kittens = 0.4(5x) = 2x and puppies = 12x/7

Total animals = 63

Total Cats=35 Kittens=14 Adult Cats=21 Total Dogs=28 Puppies=12 Adult Dogs=16

A group of 10 baby animals is chosen

No of animals =63

No of baby animals = 14+12= 26

10 babies can be selected as kittens, puppies as

(0,10) (1,9) (2,8).....(10,0)

Prob for (0,10) = 14C0(12C10)/26C10

Thus pdf would be as

(r,10-r) as 14Cr 12C(10-r)/26C10

, r = 0,1,2...10.=no of kittens

This distribution is left skewed