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2.4 Probability Distributions

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Question 36

The random variable XXX has a normal distribution with mean 12 and standard deviation 4.

a.

Find P(X<14)P(X < 14)P(X<14).

[2]
b.

Find the value of kkk such that

P(12−k<X<12+k)=0.80 P(12 - k < X < 12 + k) = 0.80 P(12−k<X<12+k)=0.80
[4]
c.

A single observation xxx, of XXX, is to be taken. A rectangle is drawn on a centimetre grid with vertices having coordinates (0,0)(0, 0)(0,0), (x,0)(x, 0)(x,0), (x,x−4)(x, x-4)(x,x−4) and (0,x−4)(0, x-4)(0,x−4).

Find the probability that the area of this rectangle is more than 45 cm245\text{ cm}^245 cm2.

[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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