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Exam-Style Question on Normal Distribution

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Question id: 10. This question is similar to one that appeared on an IB Standard paper in 2010. The use of a calculator is allowed.

The weights of players in a sports league are normally distributed with a mean of 75.2 kg, (correct to three significant figures). It is known that 75% of the players have weights between 67 kg and 80 kg. The probability that a player weighs less than 67 kg is 0.05.

(a) Find the probability that a player weighs more than 80 kg.

(b) Write down the standardized value, z, for 67 kg.

(c) Hence, find the standard deviation of weights.

To take part in a tournament, a player's weight must be within 1.5 standard deviations of the mean.

(d) Find the set of all possible weights of players that take part in the tournament.

(e) A player is selected at random. Find the probability that the player takes part in the tournament.

Of the players in the league, 22% are women. Of the women, 60% take part in the tournament.

(f) Given that a player selected at random takes part in the tournament, find the probability that the selected player is a woman.

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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.

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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