1 a problem on differencenbsptom tosses a fair die 40 times, Ask an Expert

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1. (A Problem on Difference). Tom tosses a fair die 40 times and Sara tosses a fair die 45 times. Tom wins if he can score a larger total than Sara. Find an approximation to the probability that Tom wins.

2. The proportion of impurities in a sample of water from a lake has a Beta distribution with parameters ? D ? D 2. Suppose 25 such water samples are taken. Find an approximation to the probabilities that:

(a) The average proportion of impurities in the samples exceeds .54.

(b) The number of samples for which the proportion of impurities exceeds .54 is at most 15.

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