# AP Statistics probability - binomial distribution

• Dec 24th 2009, 08:02 PM
tonycsjr16
AP Statistics probability - binomial distribution
At an archaeological site that was an ancient swamp, the bones from 20 brontosaur skeletons have been unearthed. The bones do not show any sign of disease or malformation. It is thought that these animals wandered into a deep area of the swamp and became trapped in the swamp bottom. The 20 left femur bones (thigh bones) were located and 4 of these left femurs are to be randomly selected without replacement for DNA testing to determine gender.

(a) Let X be the number of the 4 selected left femurs that are from males. Based on how these bones were sampled, explain why the probability distribution of X is not binomial.

(b) Suppose that the group of 20 brontosaurs whose remains were found in the swamp had been made up of 10 males and 10 females. What is the probability that all 4 in the sample to be tested are male?

for this one i did.. (10/20)(9/19)(8/18)(7/17) = .0433 = 4.33%

(c) The DNA testing revealed that all 4 femurs tested were from males. Based on this result and your answer from part (b), do you think that males were equally represented in the group of 20 brontosaurs stuck in the swamp? Explain.

here is where im confused!

(d) Is it reasonable to generalize your conclusion in part (c) pertaining to the group of 20 brontosaurs to the population of all brontosaurs? Explain why or why now.

confused here toooo!

This is for my apstatistics class. & it's superrr important. basically could determine if I get a B or C in the classs. please helllp!
• Dec 24th 2009, 08:10 PM
matheagle
This is wor (without replacement).
So it's hypergeometric not binomial.
The probability you computed in part (b) gives some evidence to contradict
the claim that there 10 male and 10 female dinos.
• Dec 24th 2009, 08:12 PM
tonycsjr16
so, how do you go about doing C & D?

and i'm not fimiliar with the term hypergeometric.
• Dec 24th 2009, 08:19 PM
matheagle
Quote:

Originally Posted by tonycsjr16
so, how do you go about doing C & D?

and i'm not fimiliar with the term hypergeometric.

the hypergeometric in this case, part b is....

$\displaystyle {{10 \choose 4}{10 \choose 0}\over {20 \choose 4}}={{10! \over 4!6!}\over{20!\over 4!16!}}$

That should come out to the same probability that you obtained.
YOU are selecting 4 of the 10 males AND 0 of the 10 females.
FROM a sample space that consists of 20 choose 4 dinos.

$\displaystyle ={(10)(9)(8)(7)\over (20)(19)(18)(17)}$