Quality Control Analysis using the CDF

00:00 4 marks

A car manufacturer assesses the quality of their production line by checking for defects. The probability of a car having a defect is 0.05. In a randomly selected batch of 25 cars, let X be the number of defective cars. Assuming a binomial model is appropriate, calculate the probability that at most 2 cars are defective, i.e., find P(X ≤ 2). Use a GDC with binomial cumulative distribution functions to evaluate your answer and interpret what this probability means for the manufacturer’s quality control process.

Hint Hint

Hint

Use the binomial cumulative distribution function (binomcdf) on your GDC. Identify n, p, and the upper bound for X. Alternatively, consider summing individual binomial probabilities.

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Answer Answer

Complete Answer

Approximately 0.873

Mark Scheme Mark Scheme

Answer Explanation Answer Explanation

Examiner Tips Examiner Tips

Common Errors Common Errors

Focus Focus

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