A company manufactures smartphones. A quality control inspector randomly selects 4 smartphones from each batch for testing. The probability that a smartphone is defective is 0.05. Let $X$ be the number of defective smartphones in the sample of 4.
Calculate the probability that at least one smartphone in the sample is defective. Account for how the defining parameter $p$ would affect the shape of the probability mass function if $p$ was closer to 0 or 1.
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Create Free Account Log inThis is a free VCE Units 3 & 4 Mathematical Methods practice question worth 4 marks, testing your understanding of Discrete Random Variables. It falls under Data analysis, probability and statistics in Unit 4: Mathematical Methods Unit 4. Submit your answer above to receive instant AI-powered marking and personalised feedback.
Continues the study of functions, algebra, calculus, and introduces probability and statistics.
Covers discrete and continuous random variables, probability distributions, and statistical inference for sample proportions.
discrete random variables: - specification of probability distributions for discrete random variables using graphs, tables and probability mass functions - calculation and interpretation of mean, $\mu$, variance, $\sigma^{2}$, and standard deviation of a discrete random variable and their use - Bernoulli trials and the binomial distribution, $\operatorname{Bi}(n, p)$, as an example of a probability distribution for a discrete random variable - effect of variation in the value(s) of defining parameters on the graph of a given probability mass function for a discrete random variable - calculation of probabilities for specific values of a random variable and intervals defined in terms of a random variable, including conditional probability
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A fair six-sided die is rolled. Let $X$ be the random variable representing the number rolled. State the mean and standard deviation of $X$.
A shipping company, 'CargoMax', insures its delivery vans against accidents. Historical data suggests that the number of accidents a van exp…
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