# Application of Probability in Duracell Battery Life

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1. Duracell Ltd claim that the life of their batteries in motorized soft toys is approximately normally distributed with a mean of 102.9 hours and a standard deviation of 16.5 hours. The best 65% of batteries would last beyond how many hours? Answer correct to 2 decimal places.

2. The average and standard deviation of the amount of Goods and Services tax remitted by performance artists in a twelve month period were $5.042 thous and $1.551 thous respectively. If a sample of 110 artists was taken, find the average value above which only 15% would lie. Give your answer in dollars to the nearest dollar.

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The solution gives deatiled steps on calculating the probability under the condition of normal distribution using the example of durecell battery and example of Goods and Services tax . All formula are written down with explanation.

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1. The best 65% requires that there exist one z such that P(Z>z)=1-0.65=0.35. From standard normal table, z=0.385. Now let X be the life of best 65% ...

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