E7a — AQA GCSE Statistics

Test yourself on E7a with AQA GCSE practice questions.

7 days Premium · Then free forever · No card, no charge

Your focus

Interpret data related to rates of change over time (including, but not limited to, births, deaths, house prices and unemployment) when given in graphical form.

E7a exam tips

Quick Revision Summary (Key Takeaway)

E7a covers the normal distribution in AQA GCSE Statistics: a continuous, symmetric, bell-shaped probability model defined by its mean and standard deviation. Students must standardise values using z-scores, use standard normal tables or calculator functions to find probabilities, and interpret results in real-world contexts.

How Students Lose Marks (Examiner Pitfalls)

Pitfall: Forgetting to standardise a value before using the standard normal table, or using the standard deviation instead of the variance in the notation N(μ, σ²).

❌ Weak Answer (Loses Marks):I used the mean and standard deviation directly in the table, so P(X > 140) = 0.0918.

Example improved answer:Calculate z = (x - μ)/σ = (140 - 120)/15 = 1.33 (2 d.p.). Then P(Z > 1.33) = 1 - P(Z < 1.33) = 1 - 0.9082 = 0.0918. The probability is 0.0918 (or 9.18%).

Examiner Tip: Always write the standardisation formula with values substituted. This earns method marks even if the final table lookup is wrong. Remember that N(μ, σ²) uses variance, but z-scores use the standard deviation σ.

Pitfall: Mixing up the direction of the inequality, such as finding P(X < x) when the question asks for P(X > x), or failing to interpret the probability in context.

❌ Weak Answer (Loses Marks):The probability is 0.9082, so 90.82% of apples weigh more than 140 g.

Example improved answer:We need P(X > 140). Since z = 1.33, P(Z > 1.33) = 1 - 0.9082 = 0.0918. Therefore, about 9.18% of apples are expected to weigh more than 140 g.

Examiner Tip: Sketch the normal curve, mark the mean, and shade the required area. Check whether the question asks for a decimal, a percentage, or a proportion. A final contextual sentence secures the interpretation mark.

Step-by-Step Worked Solutions

Question: The masses of apples from an orchard are normally distributed with mean 120 g and standard deviation 15 g. Find the probability that a randomly chosen apple has a mass greater than 140 g.

1.Step 1: Identify μ = 120 g, σ = 15 g, x = 140 g. We need P(X > 140).
2.Step 2: Standardise: z = (x - μ)/σ = (140 - 120)/15 = 20/15 = 1.33 (to 2 d.p.).
3.Step 3: Use standard normal table: P(Z < 1.33) = 0.9082. So P(Z > 1.33) = 1 - 0.9082 = 0.0918.
4.Step 4: State conclusion: The probability is 0.0918 (or 9.18%).

Final Answer: P(X > 140) = 0.0918 (9.18%).

Question: A machine fills bags of sugar. The masses are normally distributed with mean 1.00 kg and standard deviation 0.02 kg. Find the probability that a bag has a mass between 0.97 kg and 1.03 kg.

1.Step 1: μ = 1.00 kg, σ = 0.02 kg, x1 = 0.97 kg, x2 = 1.03 kg. Need P(0.97 < X < 1.03).
2.Step 2: Standardise both values: z1 = (0.97 - 1.00)/0.02 = -1.50; z2 = (1.03 - 1.00)/0.02 = 1.50.
3.Step 3: Use table: P(Z < 1.50) = 0.9332; P(Z < -1.50) = 0.0668. So P(-1.50 < Z < 1.50) = 0.9332 - 0.0668 = 0.8664.
4.Step 4: The probability is 0.8664 (or 86.64%).

Final Answer: P(0.97 < X < 1.03) = 0.8664 (86.64%).

Your focus

E7a exam tips

More AQA GCSE Statistics topics

Cookies on MasteryMind