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.
