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.
390 exam-style questions on OCR (MEI) A Level Maths 2.4 Probability Distributions, covering 2.4.1 Recognise binomial situations, 2.4.2 Probability of success p, 2.4.3 Calculate binomial probabilities, 2.4.4 Mean of the binomial distribution, 2.4.5 Expected frequencies for binomial, 2.4.6 Probability functions and discrete random variables, 2.4.7 Numerical probabilities for a simple distribution, 2.4.8 Normal distribution as a model (A-level only), 2.4.9 Shape of the Normal curve (A-level only), 2.4.10 Linear transformation and standardising (A-level only), 2.4.11 Symmetry and inflection of Normal curve (A-level only), 2.4.12 Calculate probabilities from a Normal distribution (A-level only), 2.4.13 Model with probability distributions, and 2.4 Probability Distributions. Each one has a worked solution and a mark scheme showing where the marks go.