The yield of a specific chemical reaction, YYY grams, is modeled by a normal distribution such that Y∼N(120,152)Y \sim \text{N}(120, 15^2)Y∼N(120,152).
Determine the probability that a randomly selected batch results in a yield of less than 138 g.
Calculate the upper quartile, Q3Q_3Q3, of the yield YYY.
Using the symmetry of the distribution, write down the lower quartile, Q1Q_1Q1, of YYY.
An outlier in this process is defined as any yield YYY such that Y<hY < hY<h or Y>kY > kY>k, where
h=Q1−1.5×(Q3−Q1)andk=Q3+1.5×(Q3−Q1) h = Q_1 - 1.5 \times (Q_3 - Q_1) \quad \text{and} \quad k = Q_3 + 1.5 \times (Q_3 - Q_1) h=Q1−1.5×(Q3−Q1)andk=Q3+1.5×(Q3−Q1)Calculate the value of hhh and the value of kkk.
Find the probability that a randomly selected batch yield is classified as an outlier.
Practise Edexcel A Level Maths The Normal Distribution with exam-style questions for A Level Maths. 439 questions, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
