AQA Paper 3 2019 June — Question 17

Exam BoardAQA
ModulePaper 3 (Paper 3)
Year2019
SessionJune
TopicNormal Distribution
TypePercentages or proportions given

17 Elizabeth's Bakery makes brownies. It is known that the mass, \(X\) grams, of a brownie may be modelled by a normal distribution.
\(10 \%\) of the brownies have a mass less than 30 grams.
\(80 \%\) of the brownies have a mass greater than 32.5 grams.
17
  1. Find the mean and standard deviation of \(X\).
    1. Find \(\mathrm { P } ( X \neq 35 )\)
      17
  2. (ii) Find \(\mathrm { P } ( X < 35 )\)
    17
  3. Brownies are baked in batches of 13.
    Calculate the probability that, in a batch of brownies, no more than 3 brownies are less than 35 grams. You may assume that the masses of brownies are independent of each other.
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