In an agricultural study, the sugar concentration of a certain variety of sugar beets, SSS, is modelled by a normal distribution with mean μ=165\mu = 165μ=165 g/L and standard deviation σ=12\sigma = 12σ=12 g/L.
Find an estimate for the proportion of beets that have a sugar concentration of less than 144 g/L.
The study selects beets for a premium processing trial. All beets are tested, and the 12% with the highest sugar concentration qualify for the trial.
Find an estimate for the minimum sugar concentration required to qualify for the trial. Give your answer correct to 4 significant figures.
Find an estimate for the median sugar concentration of the beets that qualify for the trial.
Qualified beets undergo a secondary extraction process. The concentration achieved in the secondary process is independent of the first and follows the same normal distribution. Beets that achieve a concentration greater than 186 g/L in this secondary process are categorized as "Elite".
At the start of the study, a beet is selected at random.
Find the probability that this beet will be categorized as "Elite".
