Binomial distribution - practice problems

The binomial distribution is a discrete probability distribution modeling the number of successes in a fixed number of independent trials, each with the same probability of success. Characterized by parameters n (number of trials) and p (probability of success), the probability of exactly k successes is P(X=k) = C(n,k)·p^k·(1-p)^(n-k). The mean is μ = np and variance is σ² = np(1-p). This distribution applies when trials are independent, each has only two outcomes (success/failure), and the probability remains constant. Applications include quality control, clinical trials, survey analysis, and any scenario involving repeated yes/no experiments. The binomial distribution approximates a normal distribution for large n, facilitating statistical inference.

Instructions: Solve each problem carefully and provide a detailed solution for every item.

Number of problems found: 133

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