# Exam-Style Question on Normal Distribution

## A mathematics exam-style question with a worked solution that can be revealed gradually

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Question id: 81. This question is similar to one that appeared on an IB Studies paper in 2014. The use of a calculator is allowed.

The heights of palm trees along a beach are normally distributed with a mean of 4.55m and a standard deviation of 0.37m.

(a) Find the probability that a randomly chosen tree has a height greater than 4.55m.

(b) Find the probability that a randomly chosen tree will be within 2 standard deviations of the mean. Give your answer as an integer percentage.

(c) Use your graphic display calculator to calculate the probability that a randomly chosen tree will have a height greater than 4m.

(d) The probability that a particular tree is less than $$x$$ metres tall is 0.75. Find the value of $$x$$.

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If you are using a TI-nSpire CX calculator and you would like to see an example of the process used in this question see GDC Essentials. If you would like to interact with the graph of the normal distribution you will find it waiting for you on the Graph Plotter.

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