QCEVault

Continuous random variables and the normal distribution — Question 324

Original QCE Vault practice · 8 marks

Q324 · Practice questionTechnology-freeComplex unfamiliar8 marks

QUESTION 324 (8 marks)

A small stage drone repeats a vertical routine h(t)=3+2sin⁡(πt/6)h(t)=3+2\sin(\pi t/6) metres, where tt is measured in seconds, for 0≤t≤120\leq t\leq12. A photograph is taken at a random time TT uniformly distributed on [0,12][0,12].
Height graph h(t)=3+2 sin(pi t/6) over one 12-second period. The level h=4 is dashed.
a)
Determine the maximum vertical speed of the drone.
[2 marks]
b)
Determine P(h(T)>4)P(h(T)>4) exactly.
[3 marks]
c)
Determine the exact height HH such that P(h(T)≤H)=0.95P(h(T)\leq H)=0.95.
[3 marks]
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