Math Problem Statement

Suppose	22%	of	the	1,300	fish	in	a	lake	have	been	

tagged as part of a study. We capture and release 12 fish, with replacement. Let X = the number of tagged fish we capture. Answer the following: a) (6 points) Specify the distribution of X: X ~ ________________________ b) (6 points) What is the expected value of X? (Round to one decimal place.) c) (9 points) What is the probability of getting 4 or more tagged fish? That is, compute P(X ≥ 4). Give the value as a probability (not percentage) rounded correctly to three decimal places.

Solution

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Probability
Binomial Distribution
Expected Value
Cumulative Probability

Formulas

Binomial distribution: P(X=k) = C(n, k) * p^k * (1-p)^(n-k)
Expected value of binomial distribution: E(X) = n * p
Cumulative probability: P(X ≥ k) = 1 - P(X < k)

Theorems

Binomial Theorem
Law of Total Probability

Suitable Grade Level

Grades 10-12