Mark normal-category regions and determine two boundary quantiles.

Mark normal-category regions and determine two boundary quantiles.

7 marks
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The heights of certain plants are normally distributed. The plants are classified into three categories. The shortest 12.92% are in category A. The tallest 10.38% are in category C. All the other plants are in category B with heights between r cm and t cm.

  1. Complete the following diagram to represent this information.[2]
  2. Given that the mean height is 6.84 cm and the standard deviation 0.25 cm, find the value of r and of t.[5]

Solution:

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Answer:Thus \(r=6.84-1.13(0.25)=6.56\) cm and \(t=6.84+1.26(0.25)=7.16\) cm.

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