During Halloween in a particular part of the city, it is noted that at the end of the night the weight of a child’s Trick or Treat bag is normally distributed with a population mean weight of 10 lbs and a population standard deviation of 3 lbs. At the end of Halloween night: a. If a child is selected at random, find the probability their bag weighs less than 9 lbs.
b. If a child is selected at random, find the probability their bag weighs between 9 and 12 lbs.
c. Find the 80th percentile of treat bag weights. Interpret the 80th percentile.
At the end of Halloween night suppose a sample of 9 children are randomly selected:
d. Determine the sampling distribution of the sample mean weight of Trick or Treat bags for samples of size 9.
e. Find the probability that the sample mean weight of nine randomly selected Trick or Treat bags is between 9 and 12 lbs.