A laboratory study recorded the yield of a refined chemical, YYY grams, from 200 independent reaction trials. The results were summarized as follows:
∑y=8460and∑y2=454660 \sum y = 8460 \quad \text{and} \quad \sum y^2 = 454660 ∑y=8460and∑y2=454660(i) Calculate the mean yield, yˉ\bar{y}yˉ. (ii) Determine the standard deviation of the yield.
Assuming the yield YYY is normally distributed based on these parameters, find: (i) P(30<Y<55)P(30 < Y < 55)P(30<Y<55) (ii) P(Y=45.0)P(Y = 45.0)P(Y=45.0)
Determine with a reason whether the normal distribution is an appropriate model for the yield in this study.
In a separate process using a different catalyst, the yield WWW grams follows a normal distribution with a standard deviation of 5.4. Given that the probability of the yield exceeding 40 grams is 0.015, calculate the mean yield μW\mu_WμW for this process, providing your answer to three significant figures.
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.