A population consists of the four numbers 3, 7, 11, 15. Consider all possible samples of size two which can be drawn without replacement from this population. Find (a) the population mean, (b) the population standard deviation, (c) the mean of the sampling distribution of means, (d) the standard deviation of the sampling distribution of means. Verify (c) and (d) directly from (a) and (b) by use of suitable .formulate

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Asphalt Binders and Mixtures

Asphalt binders are subsidiary products procured during the refining process of petroleum while manufacturing gasoline, diesel, and similar petroleum products. Asphalt binders are obtained from the residue that remains after the distillation of petroleum, this residue is further subjected to steam distillation and oxidation to remove the traces of gas oil present in the residue. Certain additives or modifiers are also added to asphalt binders to alter them to suit different applications.