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.
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.