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Statistics Question: Please show how to do work or plug into calculator!?

One environmental group did a study of recycling habits in a California communityIt found that 73% of the aluminum cans sold in the area were recycled(Round your answers to four decimal places.)(a) If 393 cans are sold today, what is the probability that 300 or more will be recycled? (b) Of the 393 cans sold, what is the probability that between 260 and 300 will be recycled?

Answer:

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Alli These are proportion problems a) If 393 cans are sold today, what is the probability that 300 or more will be recycled? First, make this a proportion where p 300/393 0.76336 Another formula trick P(X 300) P(p 0.76336) 1 - P(p 0.76336), now find the probability P(p 0.76336) P{ z (0.76336 - 0.73) / sqrt [(0.73)(1-0.73) / 393] } P(z 1.49) Use your TI-84 P(z 1.49) DISTR normalcdf(-1E99,1.49) 0.9319 Answer: 1 - 0.9319 0.0681 (b) Of the 393 cans sold, what is the probability that between 260 and 300 will be recycled? Again, convert to proportions p1 260/393 0.66158 p2 0.76336 P(260 X 300) P(0.66158 p 0.76336), now use our trick P(0.66158 p 0.76336) P(p 0.76336) - P(p 0.66158), and again calculate each probability P(p 0.76336) P{z (0.76336 - 0.73) / sqrt [(0.73)(1-0.73) / 393] } P(z 1.49) P(z 1.49) 0.9319 [from (a) above] P(p 0.66158 ) P{z (0.66158 - 0.73) / sqrt [(0.73)(1-0.73) / 393] } P(z -3.055) P(z -3.055) DISTR normalcdf(-1E99,-3.055) 0.0011 Final Answer 0.9319 - 0.0011 0.9308 hope that helped

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