A manufacturing lab monitors the volume and composition of industrial coolant.
The volume, VVV ml, of a standard canister is modeled by a normal distribution with a mean of 450.5450.5450.5 and a standard deviation of 2.42.42.4.
Find the probability that a randomly selected canister contains exactly 450.5450.5450.5 ml of coolant.
Find the probability that a randomly selected canister contains more than 448.0448.0448.0 ml.
The mass, MMM grams, of the active chemical concentrate in a batch is modeled by a normal distribution with mean μ\muμ and standard deviation σ\sigmaσ.
Given that P(M<215.5)=0.85P(M < 215.5) = 0.85P(M<215.5)=0.85, show that
215.5−μ=1.036σ 215.5 - \mu = 1.036\sigma 215.5−μ=1.036σwhere the constant is given to three decimal places. Fully justify your answer.
Given further that P(M<202.0)=0.08P(M < 202.0) = 0.08P(M<202.0)=0.08, find the values of μ\muμ and 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.