The random variable XXX is normally distributed with mean μ\muμ and variance 252525. Given that P(μ−3k<X<μ+3k)=0.7P(\mu - 3k < X < \mu + 3k) = 0.7P(μ−3k<X<μ+3k)=0.7:
find the value of kkk.
The random variable YYY is normally distributed with mean μ\muμ and standard deviation σ\sigmaσ. Given that 3μ=4σ23\mu = 4\sigma^23μ=4σ2 and P(Y>54μ)=0.0228P\left(Y > \frac{5}{4}\mu\right) = 0.0228P(Y>45μ)=0.0228: find the value of μ\muμ and the value of σ\sigmaσ.
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.