# Exam Style Question

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

### Probability Normal Binomial

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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