Automated security software monitors login attempts for potential breaches. For a specific category of low-risk attempts, the probability that the software fails to flag the attempt is 0.06. A security audit reviews these attempts in independent blocks of 50.
Determine the probability that a single block of 50 contains no more than 2 unflagged attempts.
The auditor evaluates 12 such independent blocks. Find the probability that fewer than 3 of these blocks contain at most 2 unflagged attempts.
Using a suitable approximation, estimate the probability that the total number of unflagged attempts across the 12 blocks is more than 45.
67 exam-style questions on OCR A Level Maths 2.4.4 Mean and variance of the binomial (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.