Question

[ Question # 3 Ni-101 siol lao Marks CLO Due Date: Tuesday, February 12, 2019 at 4:30 A.M. Clearly state all necessary assumptions and equations required for your calculations No consultation or group work is permitted. 1) The folowing table shows the sample data of outage times for a distribution transformer in hours. Each row represents the data assigned for each student according to the last 3 digits ofthe student ID. number. l.D.# 1 10 95 21 096 09 17 16 10 17 13 23 1313 27 114 20 14 13 15 13 15 16 26 26 Calculate the following: a) Arithmetic mean b) Geometric mean c) Standard deviation d) Variance e) Compute the 95 % confidence interval for the arithmetic mean.

Answer 1

For example, Take an ID number 094 For ID # 094 n = 6 p = 0 . 17 q = 1 - p = 1 - 0 . 17 = 0 . 83 (a) The probability that no generator will fail during the day is given by the binomial distribution Let x be a random variable which gives the number of generator that fail during the day we want p(x = 0) p(x = 0) = n_c_0 (p) degree (q)^n - 0 p(x = 0) = 6c_0 (0 . 17) degree (0 . 83)^6 = (1) (1) (0 . 83)^6 p(x = 0) = 0 . 326 The probability that no generator will fail during the day is p(x = 0) = 0 . 326 (b) probability that no more than 3 generators will fail is given by p(x lessthanorequalto 3) = p(x = 0) + p(x = 1) + p(x = 2) + p(x = 3) = 6c_0 (0 . 17) degree (0 . 83)^6