E8b — AQA GCSE Statistics

Test yourself on E8b with AQA GCSE practice questions.

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Make comparisons of correlation by inspection: strong or weak.

E8b exam tips

Quick Revision Summary (Key Takeaway)

E8b in AQA GCSE Statistics focuses on using the normal distribution to calculate probabilities. You standardise a value using z = (x - μ) / σ and then use the standard normal distribution table or a calculator to find probabilities, interpreting them in context.

How Students Lose Marks (Examiner Pitfalls)

Pitfall: Students often forget to standardise the value before using the standard normal table, or they use the wrong tail of the distribution.

❌ Weak Answer (Loses Marks):For a normal distribution with mean 50 and standard deviation 10, the probability that X is less than 65 is found by reading the table at 65, giving 1.0000.

Example improved answer:First standardise: z = (65 - 50) / 10 = 1.5. Then use the standard normal table to find P(Z < 1.5) = 0.9332. So the probability is 0.9332.

Examiner Tip: Always write down the standardisation formula, substitute clearly, and sketch a bell curve to confirm which area you need.

Pitfall: Misreading the question when asked for a probability greater than a value or between two values, leading to an incorrect complement or subtraction.

❌ Weak Answer (Loses Marks):For P(X > 65), a student writes P(Z < 1.5) = 0.9332.

Example improved answer:P(X > 65) = P(Z > 1.5) = 1 - P(Z < 1.5) = 1 - 0.9332 = 0.0668. For a between question, subtract the smaller cumulative probability from the larger one.

Examiner Tip: Underline the direction words: 'less than', 'greater than', 'between'. Use symmetry and complements to avoid losing method marks.

Step-by-Step Worked Solutions

Question: The masses of apples from a farm are normally distributed with mean 120 g and standard deviation 15 g. Find the probability that a randomly chosen apple has a mass less than 150 g.

1.Step 1: Identify given facts: μ = 120 g, σ = 15 g, x = 150 g.
2.Step 2: Standardise: z = (x - μ) / σ = (150 - 120) / 15 = 2.0.
3.Step 3: Use the standard normal table: P(Z < 2.0) = 0.9772.
4.Step 4: State final conclusion: the probability is approximately 0.9772 or 97.72%.

Final Answer: 0.9772

Question: The lifetimes of a brand of light bulb are normally distributed with mean 1000 hours and standard deviation 80 hours. Find the probability that a randomly chosen bulb lasts between 900 and 1100 hours.

1.Step 1: Identify μ = 1000, σ = 80, lower x = 900, upper x = 1100.
2.Step 2: Standardise both values: z1 = (900 - 1000) / 80 = -1.25, z2 = (1100 - 1000) / 80 = 1.25.
3.Step 3: Find P(-1.25 < Z < 1.25) = P(Z < 1.25) - P(Z < -1.25).
4.Step 4: From table, P(Z < 1.25) = 0.8944 and P(Z < -1.25) = 1 - P(Z < 1.25) = 0.1056.
5.Step 5: Subtract: 0.8944 - 0.1056 = 0.7888.

Final Answer: 0.7888

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