18 In a particular year, the height of a male athlete at the Summer Olympics has a mean 1.78 metres and standard deviation 0.23 metres.
The heights of \(95 \%\) of male athletes are between 1.33 metres and 2.22 metres.
18
- Comment on whether a normal distribution may be suitable to model the height of a male athlete at the Summer Olympics in this particular year.
18 - You may assume that the height of a male athlete at the Summer Olympics may be modelled by a normal distribution with mean 1.78 metres and standard deviation 0.23 metres.
18
- Find the probability that the height of a randomly selected male athlete is 1.82 metres.
18
- (ii) Find the probability that the height of a randomly selected male athlete is between 1.70 metres and 1.90 metres.
18 - (iii) Two male athletes are chosen at random.
Calculate the probability that both of their heights are between 1.70 metres and 1.90 metres.
18
- The summarised data for the heights, \(h\) metres, of a random sample of 40 male athletes at the Winter Olympics is given below.
$$\sum h = 69.2 \quad \sum ( h - \bar { h } ) ^ { 2 } = 2.81$$
Use this data to calculate estimates of the mean and standard deviation of the heights of male athletes at the Winter Olympics.
[0pt]
[3 marks]
18 - Using your answers from part (c), compare the heights of male athletes at the Summer Olympics and male athletes at the Winter Olympics.
[0pt]
[2 marks]
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