Question

26. A large survey found that an American family generates an average of 17.6 lb of glass garbage each year. Assume normal distribution with the standard deviation of 3.5 pounds. a. What proportion of families generates less than 17 lbs of glass garbage each year? b. If a family is selected at random, what is the probability that it generated less than 17 lbs of glass garbage in a year? c. If a sample of 35 families is randomly selected, what is the probability that the sample mean is below 17 lb?

Answer 1

Solution: given that Let x be the glass garbage generated by the american Family meon M-17.6 standard deviation 0:3.5 N~ (17.6,3.52) The polo portion of families generates less than 17 lbs of glass garbage each year. P(x<17) 17-17.6 P(x-h. = P(Z<-01714285) - P 3.5 - 0.4319 .: 43.19% of pamilies gencrate less than 17 lbs of glass garbage each year. The probability that it generated less than 17 lbs of glass garbage in a year PCX517) - 0.4319 Therefore, the probability that it generated less than 17 Ile of glass garbage in a year for a Selected Familiy is 0:4319

The probability that the sample mean below 17 lbs is 7 = 35 55-M za - 1716 - 3.5 135 -0.6 0.59160797 :-101418511992. PC*< 17 )- P(28-10141851) = 011552 Thus, The' probability that the sample meon is below 17 lbs is O: 1552