1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
borishaifa [10]
3 years ago
15

Five individuals from an animal population thought to be near extinction in a certain region have been caught, tagged, and relea

sed to mix into the population. After they have had an opportunity to mix, a random sample of 10 of these animals is selected. Let X- the number of tagged animals in the second sample. Suppose there are actually 25 animals of this type in the region.
a. What is the distribution of X?
b. Compute the values for E(X) and Var(X)
c. What is the probability that none of the animals in the second sample are tagged?
d. What is the probability that all of the animals in the second sample are tagged?
Mathematics
1 answer:
Talja [164]3 years ago
4 0

Answer:

a) For this case the random variable X follows a hypergometric distribution.

b) E(X)= n\frac{M}{N}=10 \frac{5}{25}=2

Var(X)=n \frac{M}{N}\frac{N-M}{N}\frac{N-n}{N-1}=10\frac{5}{25}\frac{25-5}{25}\frac{25-10}{25-1}=1

c) P(X=0)= \frac{(5C0)(25-5 C 10-0)}{25C10}=\frac{1*184756}{3268760}=0.0565

d) P(X=5)= \frac{(5C5)(25-5 C 10-5)}{25C10}=\frac{1*15504}{3268760}=0.00474

Step-by-step explanation:

The hypergometric distribution is a discrete probability distribution that its useful when we have more than two distinguishable groups in a sample and the probability mass function is given by:

P(X=k)= \frac{(MCk)(N-M C n-k)}{NCn}

Where N is the population size, M is the number of success states in the population, n is the number of draws, k is the number of observed successes

The expected value and variance for this distribution are given by:

E(X)= n\frac{M}{N}

Var(X)=n \frac{M}{N}\frac{N-M}{N}\frac{N-n}{N-1}

a. What is the distribution of X?

For this case the random variable X follows a hypergometric distribution.

b. Compute the values for E(X) and Var(X)

For this case n=10, M=5, N=25, so then we can replace into the formulas like this:

E(X)= n\frac{M}{N}=10 \frac{5}{25}=2

Var(X)=n \frac{M}{N}\frac{N-M}{N}\frac{N-n}{N-1}=10\frac{5}{25}\frac{25-5}{25}\frac{25-10}{25-1}=1

c. What is the probability that none of the animals in the second sample are tagged?

So for this case we want this probability:

P(X=0)= \frac{(5C0)(25-5 C 10-0)}{25C10}=\frac{1*184756}{3268760}=0.0565

d. What is the probability that all of the animals in the second sample are tagged?

So for this case we want this probability:

P(X=5)= \frac{(5C5)(25-5 C 10-5)}{25C10}=\frac{1*15504}{3268760}=0.00474

You might be interested in
Please helppp (NO LINKS!!!)
n200080 [17]

Answer:

DE = 39.64840676

CE = 35.3269891

Step-by-step explanation:

SOH CAH TOA

Thus,

sin(27) = 18/DE

tan(27) = 18/CE

DE = 39.64840676

CE = 35.3269891

4 0
2 years ago
Is the equation below written in standard form? If not, select which explanation best applies to why the equation
natita [175]

Answer:

D

Step-by-step explanation:

The equation of a line in standard form is

Ax + By = C ( A is a positive integer and B, C are integers

12 = 2x + 4y , that is

2x + 4y = 12 ← is in standard form

8 0
2 years ago
Please help me with this.... 4x+3=23​
MArishka [77]

Answer:

x=5

Step-by-step explanation:

23-3= 4x or 20

that means 4x is equal to 20

20 divided by 4 is 5

so x is equal to 5

6 0
3 years ago
A taxi driver charges a flat rate of $3.50 plus an additional $1.65 per mile. If Mohammad wants to spend, at most, $60, how far
Ilya [14]

Answer:

A. 34 miles

Step-by-step explanation:

First, you want to subtract $3.50 from $60. Now you have $56.50. Now you want to divide that by $1.65, to see how many miles you can achieve with your price limit. So, now you have a grand total of 34.24. You round that, and you finally have your answer.

The answer to this problem is A. 34 miles

4 0
3 years ago
Please i need help. show work
Nadya [2.5K]
Just download the app photomath it helps a lot with equations plus it shows u how to do them
7 0
3 years ago
Other questions:
  • John owns a hot dog stand. He has found that his profit is represented by the equation p(x)=-x^2+62x+77, with p being profits an
    14·2 answers
  • A house has decreased in value by 26% since purchased if its current value is 185,00 what was its value when it was purchased
    6·1 answer
  • A bag has 14 yellow Marbles and 6 red marbles half of the red marbles are made of plastic a marble is selected at random from th
    7·1 answer
  • This Question: 1 pt
    10·1 answer
  • Which of the following equations represents a linear function?
    12·2 answers
  • Please help :))))))))))
    9·1 answer
  • Solve each system by elimination.
    10·1 answer
  • HELP!!! ITS TIMED!!!! Please explain the answer!!
    14·1 answer
  • What is the solution to the system below? <br> y = -3x - 2<br> 6x + 2y = -4
    5·1 answer
  • Please give explanation too! It’s angles! TwT thankies
    13·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!