Mathematical Methods · Unit 3 · Discrete random variables · Binomial distributions
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A quality-control inspector tests a batch of electronic components. Each component has a $0.08$ probability of being defective. If a random sample of $20$ components is selected from a large batch, which probability is most likely represented by a binomial distribution model for the number of defective components in the sample?
A quality control inspector tests a batch of electronic components. Historical data shows that $5\%$ of components manufactured by a particular machine are faulty. The inspector randomly selects $20$ components and tests each one. The number of faulty components in the sample follows a binomial distribution. What is the probability that exactly $3$ components in the sample are faulty?
A software company reports that 40% of users adopt their new feature within the first month of release. The company releases a new feature and monitors 50 randomly selected users over the first month. Let X be the binomial random variable representing the number of users who adopt the new feature. Calculate the probability that the number of users adopting the feature will be within one standard deviation of the mean for X.