A processor of carrots cuts the green top off each carrot wa

A processor of carrots cuts the green top off each carrot, washes the carrots, and inserts six to a package. Twenty packages are inserted in a box for shipment. To test the weight of the boxes, a few were checked. The mean weight was 20.4 pounds; the standard deviation, 0.5 pounds. How many boxes must the processor sample to be 90 percent confident that the sample mean does not differ from the population mean by more than 0.2 pounds?

Solution

You need the formula for finding the population. In words, because yahoo keeps screwing up my symbols, you need to find the z domain number for alpha divided by 2 times the standard deviation then divide that by the maximum probable error or E then square the final quotient. You are going to need a students t distribution table in order to do this. You want a 95 percent confidence. So, your alpha is 1-95=.05. Divide this by two and you get .025. The z value for this number is 1.96. You then multiply this by .5 and divide the product by .2. Why? because your standard deviation was .5 and E was .2. You should get 4.9. We now square this quotient and obtain 24.01.