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4.2 Statistical distributions (A-level only)

4.2 Statistical distributions (A-level only)

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Question 212

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

4.2 Statistical distributions (A-level only) Questions

  1. A Level
  2. /Maths
  3. /4.2 Statistical distributions (A-level only)

328 exam-style questions on WJEC A Level Maths 4.2 Statistical distributions (A-level only), covering 4.2.1 Statistical distributions (A-level only), 4.2.2 Statistical distributions (A-level only), and 4.2.3 Statistical distributions (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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