Analyzing Bernoulli Trial Data

00:00 4 marks

A quality control team in a factory tests 150 items produced on a manufacturing line. Each item is independently defective with a probability of 0.07. Based on the binomial model, the expected number of defective items is computed as \(E[X] = n \times p\). In the observed data, 10 items were defective. Compare the theoretical expected frequency with the observed frequency and state whether the data supports the assumption that the process follows a binomial distribution.

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Hint

Calculate the expected number of defects using \(E[X] = n \times p\) and compare it with 10.

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Complete Answer

Yes; since the expected number of defects is approximately 10.5 and the observed count is 10, the small difference supports the binomial model.

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