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
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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
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