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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: 80. This question is similar to one that appeared on an IB Standard paper in 2014. The use of a calculator is allowed.

Eels are elongated fish, ranging in length from 5cm to 4m. In a certain lake the length of the eels are normally distributed with a mean of 84cm and a standard deviation of 18cm. Eels are classified as giant eels if they are more than 120 cm long.


An eel is selected at random from the lake.

(a) Find the probability that this eel is a giant.

(b) Given that this eel is a giant, find the probability that it is longer than 130cm.

(c) Two eels are selected at random. Find the probability that they are both giants.

100 eels are selected at random.

(d) Find the expected number of these eels that are giants.

(e) Find the probability that at least 5 of these eels are giants.

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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.

The exam-style questions appearing on this site are based on those set in previous examinations (or sample assessment papers for future examinations) by the major examination boards. The wording, diagrams and figures used in these questions have been changed from the originals so that students can have fresh, relevant problem solving practice even if they have previously worked through the related exam paper.

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