THE UNIVERSITY OF SYDNEY SCHOOL OF MATHEMATICS AND STATISTICS Semester 1 MATH1015 (BIOSTATISTICS) ASSIGNMENT 2013 Important: This assignment will be worth 5% towards your nal raw mark. This will be due on Tuesday 30 April. See the course Information Sheet/pages 27-28 of the Junior Mathematics Handbook for details relating to the submission. If you use R to answer any question, then attach the R output with all commands. Note: Write your answers clearly giving all necessary steps to secure full marks. A signed assignment cover sheet must be attached to your folder with your name and SID. 1. Following are the total scores of three subjects of seventy four year 8 students from a high school. 10 1 4 6 7 8 9 11 0 2 3 3 3 6 8 8 8 9 12 0 0 0 0 1 1 2 2 3 4 6 7 13 3 3 4 5 6 7 7 9 9 14 0 1 2 5 7 7 9 15 0 2 3 4 8 9 16 1 4 6 6 8 17 0 7 7 9 18 1 4 8 19 4 5 7 20 3 4 6 21 2 4 22 3 6 23 8 24 25 26 2 (a)(i) Find the ve number summary for this data set. (ii) Determine whether there are any outliers and sketch a box-plot showing clearly thresholds and outliers (if any). (iii) Describe the shape of this distribution. (b)(i) Find the mean, variance and the coecient of variation of this data set. (ii) What proportion of total scores are within 1 standard deviation of the mean? Compare this proportion with the corresponding empirical rule and comment. 2. (a) Jonka tries to connect to his internet service provider. The probability that he connects on any single attempt is 0.85 . (i) What is the probability that he connects for the rst time on his second attempt? (ii) He decides to attempt only three times to connect to his internet. List all possible outcomes and draw a suitable tree diagram to represent this experiment. (iii) What is the probability that he is still not connected after his third attempt? …..PTO for Q2(b), (c) and Q3
(b) A particular binomial distribution, X B(n; p) has the mean 4 and variance 3. (i) Find the values of n and p: (ii) Find the probability, P(6 X 8) close…