# Statistics Assignment

**Question description**

Help me understand this problems. (1)A certain make of car Tyre can be safely used for 25,000 km on average before it is replaced. The makers guarantee to pay compensation to anyone whose Tyre does not last for 22,000 km. They expect 7.5% of all tyres sold to qualify for compensation. Assuming that the distance X travelled before a Tyre is replaced has a normal distribution, (a) Calculate, to three significant figures, the standard deviation of X. (b) Estimate the number of tyres per 1000 which will not have been replaced when they have covered 26,500 km. (2) The number of eggs laid by an insect follows a Poisson distribution with parameter 200. (a) Find the probability that (i) more than 170 eggs are laid (ii) more than 205 eggs are laid,(iii) between 180 and 240 eggs (inclusive) are laid.(b) if the probability that an egg develops is 0.1, show that the number of survivors follows a poisson distribution with parameter 20 and find the probability that there are more than 30 survivors.

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