Using CDF Tables for Binomial Distribution
A batch of components has a 20% probability of being defective. Using the binomial distribution table provided in your data booklet, determine the cumulative probability \(P(X \leq 3)\) for a sample of 12 components, where \(X\) represents the number of defective components.
Analysis of Binomial CDF and Normal Approximation
In a manufacturing process, 5% of items are defective. A quality control inspector takes a sample of 20 items. (a) Calculate the probability that at most 2 items are defective using the binomial distribution. (b) Discuss whether approximating this scenario with a normal distribution is appropriate. Justify your answer by checking the necessary conditions.
Part a
Calculate the probability that at most 2 items are defective using the binomial distribution.
Understanding Cumulative Distribution Functions for Discrete Random Variables
Explain what the cumulative distribution function (CDF) is for a discrete random variable. In your response, describe how the CDF, denoted as \(F(k)\), represents \(P(X \leq k)\) by accumulating the probabilities of all possible outcomes \(x\) that are less than or equal to a given value \(k\).