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Continuous random variables and the normal distribution — Question 328

Original QCE Vault practice · 7 marks

Q328 · Practice questionTechnology-freeComplex unfamiliar7 marks

QUESTION 328 (7 marks)

A hinged triangular shade has sides of lengths 44 m and 66 m meeting at a random angle XX radians. Its angle density is f(x)=12sin⁡xf(x)=\dfrac12\sin x for 0≤x≤π0\leq x\leq\pi, and zero otherwise.
Triangle with two sides 4 m and 6 m and included random angle X. Not to scale.
a)
Verify that ff is a valid density.
[2 marks]
b)
Determine the exact probability that the shade area is at least 63 m26\sqrt3\ \mathrm{m}^2.
[3 marks]
c)
Six independent shades use this angle model. Determine the probability that at least four meet the area requirement.
[2 marks]
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