Take Home Assignment 4 Continuous Probability Distributions Sunrise Rice The factory of Sunrise Rice fills its 5 kg bags of rice by setting a timer on an injection machine. It has been found that the weight of rice the machine puts into a bag is normally distributed with standard deviation of 0.1 kg. RICE FOTOSEARCH (a) If the company wants 99% of all bags to have at least 5 kg as printed on the bag, what mean amount should the injection machine be set to put in each bag? Question (a) 0.01. 05 1% 0.99 or 99% x ? DA Left Right Tail D Tail P= 0.99 > 5 kg 6 = 0.1 kg Find an x (mean) value to give a probability of 99% any sample will be greater than 5kg Calculator: Stat - DIST - NORM -D INVN -> Tail = Right - 1- right tail area Area = 0.01 - 1- 0.99 = 0.01 6 = 0.01 u = 5 Answer: The machine should be set to deliver 5.233 kg to ensure at least 5kg is in the bag 99% of the time. (4 marks) 1
(b) Using the mean obtained in part (a), find out (i) the lower and upper boundaries of the middle 50% of bags. (ii) the minimum volume of the top 2% of bags. Question (B) (i) ? ? 1 1 1 50% Lower Upper Calculator : STAT - DIST - NORM -D INVN Tail = central Area = 0.5 6 = 0.1 M = 5.233 : x1 (Lower) = 5.16555 x2 (upper) = 5.30044 (ii) 0.98 01 98% 0.02 or 2% Calculator: STAT -D DIST -> NORM - INUN Tail = right Area = 0.02 = 0.1 M 5.233 (6 marks) 2
You must draw graphs for each question and show all workings. Answers without correct graphs and workings will not score full marks. Submission Instructions: 1. Submit your THA as a single document in pdf format via Bb. 2. After uploading your THA, it is the student's responsibility to go back to the Assignment Upload page to check that the correct THA was properly uploaded. Due: April 1 15 (Sun) 11:59 pm (End of semester break) 3