SOLUTION: One environmental group did a study of recycling habits in a California community. It found that 75% of the aluminum cans sold in the area were recycled. (Use the normal approximat

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Question 1076183: One environmental group did a study of recycling habits in a California community. It found that 75% of the aluminum cans sold in the area were recycled. (Use the normal approximation. Round your answers to four decimal places.)
(a) If 383 cans are sold today, what is the probability that 300 or more will be recycled?

(b) Of the 383 cans sold, what is the probability that between 260 and 300 will be recycled?

Thank you!
Answer by Boreal(15235) (Show Source):
You can put this solution on YOUR website!
mean is 383*.75=287.25
variance is np(1-p)=71.81=mean*.25
sd= sqrt (V)=8.47
continuity correction factor
z=(299.5-287.25)/71.81=0.1706. and probability z>300=0.4322
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between 260 and 300
z=(259.5-287.25)/8.47=-3.34
z=(300.5-287.25)/8.47=1.56
0.9406
It is a little more than 0.50+0.4322 because of the continuity correction factor.