) A Tea Dl 3. Buildings in a certain city centre are classified by height as tal
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Question
) A Tea Dl 3. Buildings in a certain city centre are classified by height as tall, medium or short. The heights can be modelled by a normal distribution with mean 50 metres and standard deviation 16 metres. Buildings with a height of 70 metres are classified as tall. (i) Find the probability that a building chosen at random is classified as tall. 3] (ii) The rest of the buildings are classified as medium and short in such a way that there are twice as many medium buildings as there are short ones. Find the height below which buildings are classified as short. [6]Explanation / Answer
i)as z score=(X-mean)/std deviation
hence P(tall)=P(X>70)=P(Z>(70-50)/16)=P(Z>1.25)=0.1056
ii)
as P(short bulding)+P(medium buldings)=P(short bulding)+2*P(short bulding)=1-0.1056
3*P(short bulding)=0.8944
P(short bulding)=0.2981
for 0.2981 probabiliy; critical z=-0.53
therefore corresponding height=mean+z*std deviation =50-0.53*16=41.52
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