The completion times for three distinct phases of a luxury residential construction project—foundation preparation (FFF), structural framing (GGG), and interior finishing (HHH)—are assumed to follow independent normal distributions:
F∼N(40,4.52)F \sim \text{N}(40, 4.5^2)F∼N(40,4.52) G∼N(60,7.22)G \sim \text{N}(60, 7.2^2)G∼N(60,7.22) H∼N(35,6.42)H \sim \text{N}(35, 6.4^2)H∼N(35,6.42)
where the times are measured in working days.
Determine the probability that the total time required for these three phases in a randomly selected project exceeds 150 working days.
Find the probability that the structural framing phase takes at least 30 days longer than the interior finishing phase.
Given that P(F+G+H<t)=0.05P(F + G + H < t) = 0.05P(F+G+H<t)=0.05, find the value of ttt.
A construction firm is overseeing 8 independent projects of this type. Using the probability calculated in part (a), find the probability that the total time for the three phases exceeds 150 working days in at least two of these 8 projects.
An analyst suggests that the assumption of independence between F,G, F, G,\,F,G, and H H\,H within a single project is likely flawed. Explain, with a reason, whether this suggests the model used in part (d) is appropriate.
Practise Edexcel A Level Maths The Normal Distribution with exam-style questions for A Level Maths. 100 questions covering The Normal Distribution, Finding Probabilities for Normal Distributions, The Inverse Normal Distribution Function, The Standard Normal Distribution, Finding the mean and standard deviation, Approximating a Binomial Distribution, and Hypothesis Testing with the Normal Distribution, 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.