In a physics laboratory, the range of projectile motion achieved by students' apparatus is modelled by a normal distribution with mean μ=4.2\mu = 4.2μ=4.2 m and standard deviation σ=0.5\sigma = 0.5σ=0.5 m.
Find an estimate for the proportion of students who achieve a range of less than 3.53.53.5 m.
The experiment involves two trials. All students take part in the first trial and the 30%30\%30% who achieve the greatest range in their first trial qualify for the advanced second trial.
Find an estimate for the minimum range achieved in the first trial in order to qualify for the second trial. Give your answer correct to 4 significant figures.
Find an estimate for the median range achieved in the first trial by those students who qualify for the second trial.
The range of the second trial is independent of the first and follows the same normal distribution. Students who achieve a range greater than 4.94.94.9 m in their second trial receive a commendation.
At the start of the experiment, a student is selected at random.
Find the probability that this student will receive a commendation.
