Normal tail probability, an upper percentile and a shaded region representing a percentage of leaf lengths

Normal tail probability, an upper percentile and a shaded region representing a percentage of leaf lengths

6 marks

The lengths of the leaves on a certain plant are normally distributed with mean \(14\) cm and standard deviation \(1.6\) cm.

  1. Find the probability that a leaf chosen at random is longer than \(16.8\) cm.[2]
  2. It is known that \(90\%\) of the leaves are shorter than \(k\) cm. Find the value of \(k\).[2]
  3. The diagram below shows the normal curve for the lengths of the leaves. On the diagram, shade the region that represents the following statement, and mark the value \(12.9\) on the horizontal axis.
    \(75\%\) of the leaves are longer than \(12.9\) cm.[2]

Solution:

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Answer:(a) \(0.0401\) (b) \(k=16.1\) (c) \(12.9\) marked left of the mean and the region to its right shaded

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