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2.4.6 Probabilities using the normal distribution (A-level only)

2.4.6 Probabilities using the normal distribution (A-level only)

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Question 26

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

2.4.6 Probabilities using the normal distribution (A-level only) Questions

  1. A Level
  2. /Maths
  3. /2.4.6 Probabilities using the normal distribution (A-level only)

147 exam-style questions on OCR A Level Maths 2.4.6 Probabilities using the normal distribution (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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