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The Normal Distribution

The Normal Distribution

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Question 184

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

The Normal Distribution Questions

  1. A Level
  2. /Maths
  3. /The Normal Distribution

616 exam-style questions on Edexcel A Level Maths The Normal Distribution, covering 3.1 The Normal Distribution, 3.2 Finding Probabilities for Normal Distributions, 3.3 The Inverse Normal Distribution Function, 3.4 The Standard Normal Distribution, 3.5 Finding the mean and standard deviation, 3.6 Approximating a Binomial Distribution, and 3.7 Hypothesis Testing with the Normal Distribution. Each one has a worked solution and a mark scheme showing where the marks go.

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