# Exam Style Question

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

### Normal Distribution

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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