Task 5 Carter's Peanut Farm has employed you to perform a statistical analysis into the dimensional characteristics of peanuts to inform the design of a new sorting, grading and packaging plant. You are required to undertake three studies. Study 1: Estimate the mean length and weight of a peanut from Carters' latest crop. Your estimate of the mean length must be to within +/- 2 mm with an associated confidence level of 99%. You will be given real peanuts to undertake this task. You should aim to minimise the number of peanuts you measure and devise a plan to do this. Study 2 You must use the historical data (Appendix C) and determine the variation in mean peanut length from crop to crop. You must suggest 7 BTEC Assignment Brief Version 1.0 August 2016 Prepared By: BTEC Internal Assessment QDAM Approved by: Delivery Manager P Pearson a range of peanut lengths that the new grading machine must accommodate so that over 99.5% of all peanuts can be graded. Study 3 Use a logical argument to suggest a theoretical mathematical relationship between the length and weight of a peanut, then use the data values you obtained in the first study to ascertain the true relationship. You must then compare your results and attempt to explain any differences. a) Write a step by step plan of how you intend to go about this task. b) Execute your plan to obtain the results you require.\f