Two laboratories are being used to perform chemical analysis. Samples of the same material are sent to the laboratories for analysis as part of the study to determine whether or not they give, on the average, the same result. The analytical results for the two laboratories are as follows:- A 58.7 61.4 60.9 59.1 58.2 B 62.7 64.5 63.1 59.2 60.3 a. Find co-efficient of variation for each laboratory. b. Which laboratory gives more consistent performance and why? Q.3 According to the journal Chemical Engineering, an important property of a fiber is its water absorbency. A random sample of 150 pieces of cotton fiber is taken and absorbency on each piece was measured. The following frequency distribution shows the absorbency values with frequencies for each class. Absorbency Range Frequency 18.5-19.4 19.5-20.4 20.5-21.4 21.5-22.4 22.5-23.4 23.5-24.4 17 32 45 28 16 12 Find Q1 (Lower Quartile) and P78 (seventy eighth percentile) and interpret your results. Q.4 The following data are a result of an investigation as to effect of reaction temperature x on percent conversion of a chemical process y. Temperature C0 (x) 20 25 20 22 23 26 Conversion% (y) 43 78 69 73 48 78 i. Find the equation of regression line ii. Interpret y-intercept and regression co-efficient Q.5 The following distribution shows the drying times in hours of a certain brand of latex paint. Draw its frequency curve and comment on it about the trend of drying times. Drying Times (Hours) Frequency 2.0-2.4 2.5-2.9 3.0-3.4 3.5-3.9 4.0-4.4 4.5-4.9 12 15 20 25 18 10
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
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Q.2 |
Two laboratories are being used to perform chemical analysis. Samples of the same material are sent to the laboratories for analysis as part of the study to determine whether or not they give, on the average, the same result. The analytical results for the two laboratories are as follows:-
a. Find co-efficient of variation for each laboratory. b. Which laboratory gives more consistent performance and why?
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Q.3 |
According to the journal Chemical Engineering, an important property of a fiber is its water absorbency. A random sample of 150 pieces of cotton fiber is taken and absorbency on each piece was measured. The following frequency distribution shows the absorbency values with frequencies for each class.
Find Q1 (Lower
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Q.4 |
The following data are a result of an investigation as to effect of reaction temperature x on percent conversion of a chemical process y.
i. Find the equation of regression line ii. Interpret y-intercept and regression co-efficient |
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Q.5 |
The following distribution shows the drying times in hours of a certain brand of latex paint. Draw its frequency curve and comment on it about the trend of drying times.
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