# Exam-Style Question on Probability

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

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Question id: 667. This question is similar to one that appeared on an IB AA Higher paper in 2023. The use of a calculator is allowed.

The heights, H metres, of flowers called Xylothorn Blooms growing in the dense forests of Verdantem on the luminous planet Aurorion can be modelled by a normal distribution with mean 14.3 metres and standard deviation 3.9 metres.

(a) One of the flowers is selected at random. Find the probability that its height more than 15.5 metres.

According to this model, 40% of the flowers have a height between $$x$$ metres and 15.5 metres.

(b) Find the probability that a randomly selected flower has a height less than $$x$$ metres.

(c) Find the value of $$x$$.

(d) Ten flowers are selected at random.

Find the probability that no more than two of the flowers has a height less than $$x$$ metres.

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