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2.4 Probability Distributions

2.4 Probability Distributions

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Question 167

In a large residential district, it is estimated that 22% of households have installed solar panels.

a.

State two assumptions required to model the number of households with solar panels in a random sample of size nnn using a binomial distribution.

[2]
b.

Using this model, find the probability that exactly 4 households have solar panels in a random sample of 18 households.

[2]
c.

Calculate the mean and the variance of the number of households with solar panels in a random sample of 250 households.

[2]
d.

A regional council inspects a random sample of 250 households. The district is classified as 'Eco-Leading' if more than 62 households in the sample have installed solar panels.

Using a suitable approximation, find the probability that the district will be classified as 'Eco-Leading'.

[4]
Markscheme

2.4 Probability Distributions Questions

  1. A Level
  2. /Maths
  3. /2.4 Probability Distributions

390 exam-style questions on OCR (MEI) A Level Maths 2.4 Probability Distributions, covering 2.4.1 Recognise binomial situations, 2.4.2 Probability of success p, 2.4.3 Calculate binomial probabilities, 2.4.4 Mean of the binomial distribution, 2.4.5 Expected frequencies for binomial, 2.4.6 Probability functions and discrete random variables, 2.4.7 Numerical probabilities for a simple distribution, 2.4.8 Normal distribution as a model (A-level only), 2.4.9 Shape of the Normal curve (A-level only), 2.4.10 Linear transformation and standardising (A-level only), 2.4.11 Symmetry and inflection of Normal curve (A-level only), 2.4.12 Calculate probabilities from a Normal distribution (A-level only), 2.4.13 Model with probability distributions, and 2.4 Probability Distributions. Each one has a worked solution and a mark scheme showing where the marks go.

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