Your task in this project is to answer the following problems and prepare a report on your results. The material you may use to solve these problems can be obtained from anything we have studied so far in AP Statistics. In other words, you are not confined to only using techniques learned in, say, chapter ten or, say, chapter three. You may use any knowledge you have gained. Use the following information in answering all of the problems:
At the Drole Pineapple Company, managers are always interested in the sizes of the pineapples grown in the company's fields. The weights of pineapples grown in the Drole fields were approximately normally distributed with a standard deviation of 2.5 ounces. Last year, the pineapples harvested had a mean weight of 31 ounces.
1) Suppose a single pineapple is selected at random from last year's crop. What is the approximate probability that it weighs more than 35 ounces?
2) Suppose two pineapples are selected randomly and independently from last year's crop. Find the approximate probability that exactly one of the two pineapples weighs more than 35 ounces. In addition to the original information given above, it is discovered that the managers of the Drole Pineapple Company are eager to test a new irrigation system. They did this during the current year's production cycle. With this new information, answer the following:
3) How large a sample would you need to take to estimate the mean weight of the pineapples produced to within one ounce at a 92% confidence level?
4) Suppose you take an SRS of 50 pineapples is taken from this year's crop and you find that the mean weight of pineapples in the sample is 31.6 ounces. Using a 95% confidence interval, determine whether this sample provides evidence of a change in the mean weight of pineapples produced. describe your reasoning completely.
5) Based on an SRS of 50 pineapples with a mean weight of 31.6 ounces, did the new irrigation system cause an increase in the mean weights of pineapples produced? describe your answer completely.