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Analytical methods for engineers

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4)2(31-52.14)2+(16-52.14)2+(27-52.14)2+(82-52.14)2+(42-52.14)2+(57-52.14)2+(67-52.14)2+(51-52.14)2+(23-52.14)2+(56-52.14)2+(66-52.14)2+(59-52.14)2+(37-52.14)2+(62-52.14)2+(35-52.14)2+(43-52.14)2+(31-52.14)2+(57-52.14)2+(59-52.14)2+(70-52.14)2+(38-52.14)2+(47-52.14)2+(61-52.14)2]=Variance=√ [(57-48.74)2+ (40-48.74)2+ (12-48.74)2+ (24-48.74)2+ (67-48.74)2+ (47-48.74)2+ (37-48.74)2+(44-48.74)2+(71-48.74)2+(55-48.74)2+(55-48.74)2+(54-48.74)2+(53-48.74)2+(53-48.74)2+(51-48.74)2+(52-48.74)2+(55-48.74)2+(45-48.74)2+(49-48.74)2+(44-48.74)2+(46-48.74)2+(50-48.74)2+(60-48.74)2+(57-48.74)2+(63-48.74)2+(35-48.74)2+(39-48.74)2(52-48.74)2+(79-48.74)2+(59-48.74)2+(62-48.74)2+(43-48.74)2+(36-48.74)2+(34-48.74)2+(43-48.74)2+(28-48.74)2+(61-48.74)2+(42-48.74)2+(42-48.74)2+(47-48.74)2+(32-48.74)2+(33-48.74)2+(75-48.74)2+(53-48.74)2+(55-48.74)2+(45-48.74)2+(25-48.74)2+(48-48.74)2+(58-48.74)2+(84-48.74)2]=11065.62The performance of the longercells batteries is lower as compared to that of the powersure batteries. This is because the frequency of the cells that have a frequency of two is 6 for the longercell batteries as compared to 3 for the powersure batteries.There is a better way of modeling the relationship between y and x. This can be achieved by producing a cubic curve rather than a linear curve. This would have produced a better model of the relationship between x and y.a. The diameters of a random sample of 100 rivets produced by this machine in a day have a mean value of 4.76 mm. find a 95% confidence interval for the mean diameter of all the rivets produced by the machine in that day.b. The manufacturer becomes concerned if the lower 95% confidence limit falls below 4.6 mm. A random sample of 80 rivets on another day gave a mean diameter of 4.65 mm. Will the manufacturer be