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.
616 exam-style questions on Edexcel A Level Maths The Normal Distribution, covering 3.1 The Normal Distribution, 3.2 Finding Probabilities for Normal Distributions, 3.3 The Inverse Normal Distribution Function, 3.4 The Standard Normal Distribution, 3.5 Finding the mean and standard deviation, 3.6 Approximating a Binomial Distribution, and 3.7 Hypothesis Testing with the Normal Distribution. Each one has a worked solution and a mark scheme showing where the marks go.