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2.4 Probability Distributions

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Question 137

The time SSS, in minutes, taken by an automated medical system to sterilise a surgical instrument is modelled by the random variable SSS with probability density function

f(s)={32000(20s−s2)0≤s≤100otherwise f(s) = \begin{cases} \frac{3}{2000}(20s - s^2) & 0 \le s \le 10 \\ 0 & \text{otherwise} \end{cases} f(s)={20003​(20s−s2)0​0≤s≤10otherwise​
a.

Use algebraic integration to find, in minutes and seconds, the mean sterilisation time.

[4]
b.

Show that P(2<S<8)=81125P(2 < S < 8) = \frac{81}{125}P(2<S<8)=12581​.

[3]
c.

A medical facility monitors a batch of 125 sterilisation sessions.

Use a suitable approximation to find the probability that fewer than 75 of these sessions take between 2 and 8 minutes.

[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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