Question

Part IV. Practical Applications Each American uses an average of 650 pounds of paper in a year. Assuming that the distribution normal with a standard deviation of 153.50 pounds find the probability that a randomly selected American uses: a. More than 800lbs of paper in a year. Answer: b. Less than 400lbs of paper in a year. Answer: C. Between 500 and 700 pounds of paper in a year. Answer:

Answer 1

Given a normal distribution with mea u=650 and standard deviation = 1$3.50 pounds: Foon a) The probability that a randomly selected American uses more than 8001bs. of paper in a year X=650 1-800 ZI plac>800). Zso : Z = - = 800-650 : 0.977; 153.5 PCZ >0.977) = 0.5 - PC ZOO to 0.977) = 0.5 - 0:3360 PLZ>0-977) = 0.164 b) less than 400lbs of paper in a year Sz400 YEGSO ZL2=0 PCXC400) 3. PCészi) 1.2733,= 400-650 -1.63: P.(Z221) = 0.5- pizzo to zi) =05- PC Z=0 to -1-63) = 0.5-0.4484 = 0. OSI NET

ci between 500 and 700 pounds : 021-500, 1=650 2=700 I 2:0 Zz PL 500 C3C700) - PC ZECZCZ2) Zi = 01-4 = 500-650 = -150.- 700-650 53.50 -0.3259 Z2 = Ich 153:50 : 153.50 = -0.977 153.50 a PCZ<ZCE2) = PC -0.977CZ:20:325) = P 0 977 to 0) + PC z=0 to 0.325) = PCZ-o to 0977) + P(Z=0 to 0.325) 0 .164+ 0.1274 P( ZICZcZz) = 0.2914.