Exam-Style Question on Normal Distribution
A mathematics exam-style question with a worked solution that can be revealed gradually
Question id: 103. This question is similar to one that appeared on an IB Studies paper in 2014. The use of a calculator is allowed.
A group of students sat a Biology examination and a Computer Studies examination. The students' marks in the Biology examination are normally distributed with a mean of 70 and a standard deviation of 9.
(a) Draw a diagram that shows this information.
(b) Find the probability that a randomly chosen student who sat the Biology examination scored at most 70 marks.
Eric scored 82 marks in the Biology examination.
(c) Find the probability that a randomly chosen student who sat the Biology examination scored more than Eric.
The students' marks in the Computer Studies examination are normally distributed with a mean of 68 and a standard deviation of 11. Eric also scored 82 marks in the Computer Studies examination.
(d) Find the probability that a randomly chosen candidate who sat the Computer Studies examination scored less than Eric.
(e) Determine whether Eric's Computer Studies mark, compared to the other students, is better than his mark in Biology. Give a reason for your answer.
To obtain a grade A a student must be in the top 12% of the students who sat the Computer Studies examination.
(f) Find the minimum possible mark to obtain a grade A. Give your answer correct to the nearest integer.
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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.
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