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4 Unit A2 2: Applied Mathematics (A-level only)

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Question 105

The lifetime of an electronic component, in hours, is modelled by a Normal distribution with mean 1200 hours and standard deviation 150 hours.

a.

Write down P(X<1200)P(X<1200)P(X<1200), where X X\,X is the lifetime of a randomly chosen component.

[1]
b.

Find the probability that a randomly chosen component lasts longer than 1400 hours. Give your answer to 3 significant figures.

[1]
c.

Find the lifetime that is exceeded by 90% of these components. Give your answer to 3 significant figures.

[2]
d.

A new batch of 30 components is tested. The total lifetime of the 30 components is 34 800 34\,800\,34800 hours. Stating your hypotheses clearly, test at the 10% significance level whether the mean lifetime of components in the new batch has decreased. You may assume that the lifetimes are still Normally distributed with standard deviation 150 hours.

[4]
Markscheme

4 Unit A2 2: Applied Mathematics (A-level only) Questions

  1. A Level
  2. /Maths
  3. /4 Unit A2 2: Applied Mathematics (A-level only)

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