Calculate a normal tail percentage and a doorway design quantile.
Calculate a normal tail percentage and a doorway design quantile.
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In a country called Tallopia, the height of adults is normally distributed with a mean of 187.5 cm and a standard deviation of 9.5 cm.
What percentage of adults in Tallopia have a height greater than 197 cm?[3]
A standard doorway in Tallopia is designed so that 99% of adults have a space of at least 17 cm over their heads when going through a doorway. Find the height of a standard doorway in Tallopia. Give your answer to the nearest cm.[4]
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Answer:The 99th-percentile height is \(187.5+2.3263(9.5)=209.6\) cm. Adding 17 cm clearance gives \(226.6\) cm, hence a doorway height of \(227\) cm.