Edexcel 9MA0Paper 3 · Statistics4.2 Statistical distributions
The random variable .
(a)
Find .
(2 marks)(b)
Find .
(2 marks)(c)
Write down .
(1 mark)Practice · Edexcel 9MA0 · Paper 3 Statistics
A-level Maths normal distribution calculator with worked steps
Enter the mean, standard deviation and the values. You get the probability and the steps to write down.
0.8716
- X ~ N(60, 4²)
- P(55 < X < 68) = P(-1.25 < Z < 2.00)
- = 0.97725 − 0.10565 = 0.8716
Your calculator gives the probability directly; the Z line is the step to show when μ or σ is unknown.
Exam-style questions
1 of 5
Edexcel 9MA0Paper 3 · Statistics4.2 Statistical distributions
The masses of eggs from a farm are modelled as grams. An egg is 'large' if its mass is more than 63 grams.
(a)
Find the proportion of eggs that are large.
(2 marks)(b)
Eggs are packed in boxes of 12, chosen at random. Find the probability that a box contains at least 2 large eggs.
(3 marks)Edexcel 9MA0Paper 3 · Statistics4.2 Statistical distributions
The random variable . It is known that .
(a)
Write down the value of , giving a reason.
(1 mark)(b)
Find .
(2 marks)(c)
Describe where the points of inflection of the density curve are.
(1 mark)Edexcel 9MA0Paper 3 · Statistics4.2 Statistical distributions
The time minutes that customers spend in a queue is modelled as . 15% of customers queue for more than 40 minutes.
(a)
Find the value of .
(3 marks)(b)
Find the probability that a customer queues for less than 30 minutes.
(1 mark)Edexcel 9MA0Paper 3 · Statistics4.2 Statistical distributions
The lengths of leaves on a plant are modelled as cm. 5% of leaves are shorter than 12 cm and 10% are longer than 30 cm.
(a)
Find the values of and .
(5 marks)(b)
Explain how you can tell, without calculating, that must be nearer to 30 than to 12.
(1 mark)Learn each method
- Normal probabilitiesLesson in A-level Maths Pro
- Inverse Normal and unknown parametersLesson in A-level Maths Pro
Questions people ask
Do I have to standardise in A-level Maths?
Not to find a probability: your calculator gives P(a < X < b) directly. You do need Z = (X − μ) / σ when the mean or standard deviation is unknown, so write that step out.
What does N(60, 16) mean?
A Normal distribution with mean 60 and variance 16, so the standard deviation is 4. The second number is the variance, not the standard deviation.
Why is P(X = 50) zero?
X is continuous, so a single value has probability zero. That is also why P(X < 50) and P(X ≤ 50) are the same.