The independent random variables L1L_1L1 and L2L_2L2 represent the mechanical loads, in kN, applied to two different structural supports during a stress test. They are defined as L1∼N(140,42)L_1 \sim N(140, 4^2)L1∼N(140,42) and L2∼N(35,1.52)L_2 \sim N(35, 1.5^2)L2∼N(35,1.52). A differential stress index DDD is defined by the relation:
D=2L1−7L2 D = 2L_1 - 7L_2 D=2L1−7L2Find E(D)E(D)E(D).
Find Var(D)Var(D)Var(D).
The independent random variables L1,1,L1,2,…,L1,6L_{1,1}, L_{1,2}, \dots, L_{1,6}L1,1,L1,2,…,L1,6 each follow the same distribution as L1L_1L1. They are also independent of L1L_1L1 and L2L_2L2. An aggregate load variable BBB is defined as:
B=∑i=16L1,i B = \sum_{i=1}^{6} L_{1,i} B=i=1∑6L1,iCalculate P(B>30D)P(B > 30D)P(B>30D).
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.