Central Limit Theorem questions

Questions to attempt

3 questions on Central Limit Theorem, each with its mark scheme and worked method. Reveal the answer when you have had a go.

1. FS1-5.1 · Applications of the Central Limit Theorem to other distributions.

   Q1

   ORIGINAL

   Year 2

   Year 2: this is content the exam board adds beyond the AS subject content, for the full A-level.

   1.

   A geometric population has parameter $p=0.32$. A random sample of $45$ observations is taken. Find the value of $c$ for which $P(\overline X>c)\approx0.05$, giving $c$ to $3$ decimal places.

   (6)

   (Total for Question 1 is 6 marks)

   Reveal answer and method

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2. FS1-5.1 · Applications of the Central Limit Theorem to other distributions.

   Q2

   ORIGINAL

   Year 2

   Year 2: this is content the exam board adds beyond the AS subject content, for the full A-level.

   2.

   Independent lifetimes have population mean $50$ hours and variance $100$ hours$^2$. For a sample of $36$ lifetimes, use the Central Limit Theorem to estimate $P(\overline X<47.5)$.

   (4)

   (Total for Question 2 is 4 marks)

   Reveal answer and method

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3. FS1-5.1 · Applications of the Central Limit Theorem to other distributions.

   Q3

   ORIGINAL

   Year 2

   Year 2: this is content the exam board adds beyond the AS subject content, for the full A-level.

   3.

   A population has mean $\mu$ and variance $36$. Using the Central Limit Theorem normal approximation, estimate the least sample size $n$ for which $P(|\overline X-\mu|<1.2)\geq0.95$.

   (6)

   (Total for Question 3 is 6 marks)

   Reveal answer and method

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FS1-5 Central Limit Theorem revision notes