A geomechanical boring tool is used to create pilot holes for foundation piles. The depth, DDD millimetres, achieved in a single standard operation of the tool is normally distributed with mean 500500500 and standard deviation 202020.
Using standardisation, show that the probability that an operation results in a depth of less than 492 mm492 \text{ mm}492 mm is 0.34460.34460.3446.
A specific site requirement necessitates a hole depth of at least 492 mm492 \text{ mm}492 mm. A technician is permitted up to 3 independent attempts at a single location to meet this requirement. If an attempt meets or exceeds the requirement, no further attempts are made at that location.
Given that the technician eventually successfully met the requirement at a location, determine the probability that success was achieved on the second attempt with a hole deeper than 530 mm530 \text{ mm}530 mm.
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.