math

posted by .

Scientists randomly caught 30 fruit bats at an orchard. They tagged the fruit 
bats and then released them. Several weeks later, they captured 20 fruit bats at the same location. They found that 4 of those fruit bats 
had tags. Assume the population of fruit bats does not change. About how many fruit bats
 are at that orchard?

  • math -

    There are two ways to solve this problem.

    A.
    The intuitive (and fast) approximation is by prorating the ratio, assuming that the ratio is constant.
    Let N=total population, then
    N/30=20/4 => N=150

    B.
    The more accurate (and elaborate) way is to use the hypergeometric distribution. This distribution is typically used in instances where sampling is done without replacement, such as drawing cards out of a deck.
    Let
    A=recapture size = 20
    B=uncaptured size = population -20
    m=number of marked in sample (4)
    n=number of marked in the wild (30-4=26)
    then
    P(X=m)=C(A,m)*C(B,n)/C(A+B,m+n)
    C(n,r)=combination n choose r = n!/(r!(n-r)!)

    We need to find A+B.
    Substituting formula,
    P(x=4)=C(20,4)*C(B,26)/C(B+20,30)
    The value of P(x=4) is not directly known, but the maximum likelihood is when it is at the maximum for the various values of B.

    We will find that P(x=4) is at a maximum when B=129.5, which makes the total population A+B=20+129.5=149.5, quite close to our initial estimate.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. math

    a store sells 3 times more of bats then rackets. they sell a total of428 of bats and rackets. how many bats how many rackets
  2. science

    what would be the major result of long-term use of the same pesticide ona fruit orchard?
  3. Math

    BLIND BATS AT HALLOWEEN There were number of bats in a cave. Two bats can see out of right eye, Three bats can see out of left eye, Four can't see out of left eye, and Five can't see out of right eye. What is the least number of bats …
  4. math

    BLIND BATS AT HALLOWEEN There were number of bats in a cave. Two bats can see out of right eye, Three bats can see out of left eye, Four can't see out of left eye, and Five can't see out of right eye. What is the least number of bats …
  5. math

    a baseball team buys 15 bats for $405. aluminum bats cost $25 and wooden bats cost $30. how many of each type did they buy?
  6. math, inequalties

    THIS SEASON, NORA HAS 125 AT BATS IN SOFTBALL. BY THE END OF THE SEASON SHE WANTS TO HAVE AT LEAST 140 AT BATS. HOW MANY MORE AT BATS DOES NORA NEED TO REACH HER GOAL?
  7. Math

    The weights of adult long-tongued fruit bats are known to be normally distributed with a mean of 20.22 grams and a standard deviation of 3.23 grams. What is the probability that a randomly selected bat will: a) weigh at most 15 grams?
  8. Statistics

    The world’s smallest mammal is the bumblebee bat. Such bats are roughly the same size of a large bumblebee. Listed below are the weights (in grams) from a sample of these bats. Assuming that all such bats have a standard deviation …
  9. Math - Ratios

    The ratio of wood bats to metal bats at a sporting goods store is 2:7. After 10 metal bats are sold, the ratio of wood bats is 3:8. How many wood bats are there at the store?
  10. Algebra

    Two players have the same batting average. Player 1 At bats: 132 Hits: 45 Player 2 At bats: 32 Hits: 45 Player 1 gets four hits in the next five at bats. Player 2 gets three hits in the next three at bats. Who has the higher batting …

More Similar Questions