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2.4 Probability Distributions

2.4 Probability Distributions

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Question 99

The weights of newborn puppies in a specific breed, WWW grams, are normally distributed with W∼N(450,402)W \sim \text{N}(450, 40^2)W∼N(450,402).

a.

Find the probability that a randomly selected puppy weighs less than 510 g.

[2]
b.

Find the upper quartile, Q3Q_3Q3​, of WWW.

[2]
c.

Write down the lower quartile, Q1Q_1Q1​, of WWW.

[1]
d.

An outlier is defined as any value of WWW such that W<hW < hW<h or W>kW > kW>k, where

h=Q1−1.5×(Q3−Q1)andk=Q3+1.5×(Q3−Q1) h = Q_1 - 1.5 \times (Q_3 - Q_1) \quad \text{and} \quad k = Q_3 + 1.5 \times (Q_3 - Q_1) h=Q1​−1.5×(Q3​−Q1​)andk=Q3​+1.5×(Q3​−Q1​)

Find the value of hhh and the value of kkk.

[2]
e.

Find the probability that a randomly selected puppy’s weight is an outlier.

[3]
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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