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.
390 exam-style questions on OCR (MEI) A Level Maths 2.4 Probability Distributions, covering 2.4.1 Recognise binomial situations, 2.4.2 Probability of success p, 2.4.3 Calculate binomial probabilities, 2.4.4 Mean of the binomial distribution, 2.4.5 Expected frequencies for binomial, 2.4.6 Probability functions and discrete random variables, 2.4.7 Numerical probabilities for a simple distribution, 2.4.8 Normal distribution as a model (A-level only), 2.4.9 Shape of the Normal curve (A-level only), 2.4.10 Linear transformation and standardising (A-level only), 2.4.11 Symmetry and inflection of Normal curve (A-level only), 2.4.12 Calculate probabilities from a Normal distribution (A-level only), 2.4.13 Model with probability distributions, and 2.4 Probability Distributions. Each one has a worked solution and a mark scheme showing where the marks go.