Trader Joe's is a privately held chain of specialty grocery stores in the United States. Starting out as a small chain of convenience stores, it has expanded to over 340 stores as of June 2010 (Traderjoe.com). It has developed a reputation as a unique grocery store selling products such as gourmet foods, beer and wine, bread, nuts, cereal, and coffee. One of their best-selling nuts is Raw California Almonds, which are priced at $4.49 for 16 ounces. Since it is impossible to pack exactly 16 ounces in each packet, a researcher has determined that the weight of almonds in each packet is normally distributed with a mean and a standard deviation equal to 16.01 ounces and 0.08 ounces, respectively.
a. Discuss the sampling distribution of the sample mean based on any given sample size.
b. find the probability that a random sample of 20 bags of almonds will average less than 16 ounces.
c. Suppose your cereal recipe calls for no less than 48 ounces of almonds. What is the probability that three packets of almonds will meet your requirement?