Exam-Style Question on Normal Distribution
A mathematics exam-style question with a worked solution that can be revealed gradually
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.
The worked solutions to these exam-style questions are only available to those who have a Transum Subscription.
Subscribers can drag down the panel to reveal the solution line by line. This is a very helpful strategy for the student who does not know how to do the question but given a clue, a peep at the beginnings of a method, they may be able to make progress themselves.
This could be a great resource for a teacher using a projector or for a parent helping their child work through the solution to this question. The worked solutions also contain screen shots (where needed) of the step by step calculator procedures.
A subscription also opens up the answers to all of the other online exercises, puzzles and lesson starters on Transum Mathematics and provides an ad-free browsing experience.
Drag this panel down to reveal the solution
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.
©1997 - 2024 Transum Mathematics :: For more exam-style questions and worked solutions go to Transum.org/Maths/Exam/