6 In a cycling event the times taken to complete a course are modelled by a normal distribution with mean 62.3 minutes and standard deviation 8.4 minutes.
- Find the probability that a randomly chosen cyclist has a time less than 74 minutes.
- Find the probability that 4 randomly chosen cyclists all have times between 50 and 74 minutes.
In a different cycling event, the times can also be modelled by a normal distribution. \(23 \%\) of the cyclists have times less than 36 minutes and \(10 \%\) of the cyclists have times greater than 54 minutes. - Find estimates for the mean and standard deviation of this distribution.