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The Normal Distribution

The Normal Distribution

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Question 373

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

The Normal Distribution Questions

  1. A Level
  2. /Maths
  3. /The Normal Distribution

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.

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