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The Normal Distribution

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Question 4

The independent random variables X X\,X and Y Y\,Y represent the lifespans, in thousands of hours, of two types of industrial cooling fans, where X∼N(60,52)X \sim N(60, 5^2)X∼N(60,52) and Y∼N(45,42)Y \sim N(45, 4^2)Y∼N(45,42). A system efficiency parameter, AAA, is defined by the linear combination

A=2X−2Y A = 2X - 2Y A=2X−2Y

Find:

a.

E(A)E(A)E(A)

[2]
b.

Var(A)Var(A)Var(A)

[2]
c.

A batch of 5 independent fans of type X X\,X is tested. The random variable B B\,B is defined as the sum of their lifespans, B=∑i=15XiB = \sum_{i=1}^{5} X_iB=∑i=15​Xi​. Calculate the probability P(B>11A)P(B > 11A)P(B>11A).

[5]

The Normal Distribution Questions

  1. A Level
  2. /Maths
  3. /The Normal Distribution

Practise Edexcel A Level Maths The Normal Distribution with exam-style questions for A Level Maths. 439 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.

Question bank