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.
Practise Edexcel A Level Maths Finding Probabilities for Normal Distributions with exam-style questions for A Level Maths. 80 questions, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
