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Continuous random variables and the normal distribution — Question 309

Original QCE Vault practice · 3 marks

Q309 · Practice questionTechnology-activeSimple familiar3 marks

QUESTION 309 (3 marks)

Diameters XX mm of machine-made tokens are normally distributed with mean 3232 mm and standard deviation 33 mm. Tokens are accepted if a≤X≤ba\leq X\leq b. The acceptance interval is symmetric about the mean and contains 95%95\% of tokens.
Normal density centred at 32; the symmetric acceptance interval [a,b] is hatched.
a)
Determine aa and bb, to 0.10.1 mm.
[2 marks]
b)
For 20002000 independently produced tokens, determine the expected number rejected.
[1 mark]
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