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The Normal Distribution

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Question 30

A brand of LED lightbulbs claims to have a mean lifespan of 1200 hours.

An electrical engineer believes that the actual mean lifespan is less than 1200 hours.

The engineer tests a large batch of bulbs and produces the following summary data:

n=300∑x=357900∑x2=427454700 n = 300 \quad \sum x = 357900 \quad \sum x^2 = 427454700 n=300∑x=357900∑x2=427454700
a.

Find the mean and standard deviation of the sample.

[3]
b.

Carry out a hypothesis test to test the engineer's belief at the 1% significance level. State your assumptions clearly.

[5]
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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