A market investigator returns the following data: Of 1000 people consulted, 81 1 liked chocolates, 752 liked toffee and 418 liked boiled sweets, 570 liked chocolates and toffee, 356 liked chocolates and boiled sweets and 348 liked toffee and boiled sweets, 297 liked all three. Show that this information as it stands must be incorrect.

In a very hotly fought battle atleast 70% of the combatants lost an eye, atleast 75% lost an ear, atleast 80% lost an arm and atleast 85% lost a leg. How many atleast must have lost all four?

The first four moments Of a distribution about the value 4 of the variable are —l .5, 17, —30 and 108. Find the moments about mean, and Find also the moments about

(i) the origin, and

(ii) the point x 2.

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