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2.4 Probability Distributions

2.4 Probability Distributions

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Question 107

A manufacturing lab monitors the volume and composition of industrial coolant.

ai.

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.

[1]
aii.

Find the probability that a randomly selected canister contains more than 448.0448.0448.0 ml.

[2]
bi.

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=1.036σ

where the constant is given to three decimal places. Fully justify your answer.

[2]
bii.

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.

[4]
Markscheme

2.4 Probability Distributions Questions

  1. A Level
  2. /Maths
  3. /2.4 Probability Distributions

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.

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