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

### Normal Distribution

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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