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.
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.