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".
616 exam-style questions on Edexcel A Level Maths The Normal Distribution, covering 3.1 The Normal Distribution, 3.2 Finding Probabilities for Normal Distributions, 3.3 The Inverse Normal Distribution Function, 3.4 The Standard Normal Distribution, 3.5 Finding the mean and standard deviation, 3.6 Approximating a Binomial Distribution, and 3.7 Hypothesis Testing with the Normal Distribution. Each one has a worked solution and a mark scheme showing where the marks go.