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Exam-Style Question on Cumulative frequency and normal distribution

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

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Question id: 60. This question is similar to one that appeared on an IB Standard paper in 2014. The use of a calculator is allowed.

The weights in grams of 98 mice are shown in the cumulative frequency diagram. The heaviest mouse weighted 160g.

(a) Write down the median weight of the mice.

(b) Find the percentage of mice that weigh 70 grams or less.

The same data is presented in the following table.

Weights w grams0 < w ≤ 40 40 < w ≤ 8080 < w ≤ 120120 < w ≤ 160

(c) Find the value of p.

(d) Find the value of q.

(e) Use the values from the table to estimate the mean and standard deviation of the weights.

A second batch of mice are normally distributed with the same mean and standard deviation as those of the first group mentioned above.

(f) Find the percentage of the second batch of mice that weigh 70 grams or less.

(g) A sample of five mice is chosen at random from the second batch. Find the probability that at most three mice weigh 70 grams or less.

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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 the second part of this question see GDC Essentials.

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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