A Geiger counter counts the number of alpha particles from radioactive material. Over a long period of time, an average of 34 particles per minute occurs. Assume the arrival of particles at the counter follows a Poisson distribution. Find the probability that the mean of a randomly selected sample of size n=64 is between 31.7 and 35.7.

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A: 1 cyan2 blue3 red_________6 total sectorsP(blue)=2/6=1/3P(cyan)=1/6P(red)= 3/6=1/2