In a study of professional basketball players, the wing span of a player has a mean of 2.052.052.05 metres and a standard deviation of 0.120.120.12 metres.
The wing spans of 95%95\%95% of these players are found to be between 1.811.811.81 metres and 2.292.292.29 metres.
Comment on whether a normal distribution may be suitable to model the wing span of a professional basketball player in this study.
You may assume that the wing span of a professional basketball player may be modelled by a normal distribution with mean 2.052.052.05 metres and standard deviation 0.120.120.12 metres.
Find the probability that the wing span of a randomly selected player is exactly 2.102.102.10 metres.
Find the probability that the wing span of a randomly selected player is between 1.951.951.95 metres and 2.152.152.15 metres.
Two players are chosen at random. Calculate the probability that both of their wing spans are between 1.951.951.95 metres and 2.152.152.15 metres.
The summarised data for the wing spans, www metres, of a random sample of 505050 amateur basketball players is given below:
∑w=92.5and∑(w−wˉ)2=0.98 \sum w = 92.5 \quad \text{and} \quad \sum(w - \bar{w})^2 = 0.98 ∑w=92.5and∑(w−wˉ)2=0.98Use this data to calculate estimates of the mean and standard deviation of the wing spans of amateur basketball players.
Using your answers from part (c), compare the wing spans of professional basketball players and amateur basketball players.