The independent random variables AAA and BBB are defined as:
A∼N(25,62)andB∼N(12,42) A \sim \text{N}(25, 6^2) \quad \text{and} \quad B \sim \text{N}(12, 4^2) A∼N(25,62)andB∼N(12,42)The random variable XXX is defined as X=3A−2BX = 3A - 2BX=3A−2B.
Find P(X>60)P(X > 60)P(X>60).
The random variable C∼N(30,σ2)C \sim \text{N}(30, \sigma^2)C∼N(30,σ2). The random variables C1,C2,C3, and C4C_1, C_2, C_3, \text{ and } C_4C1,C2,C3, and C4 are independent and each has the same distribution as CCC.
The random variable YYY is defined as Y=∑i=14CiY = \sum_{i=1}^4 C_iY=∑i=14Ci.
Given that P(A+B+Y<140)=0.0401P(A + B + Y < 140) = 0.0401P(A+B+Y<140)=0.0401 and that A,B, and YA, B, \text{ and } YA,B, and Y are independent,
find the value of σ\sigmaσ, the standard deviation of CCC.
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.