Solutions of Exam 1 on Statistics Applied to Natural Sciences | MATH 338, Exams of Mathematics

Download Solutions of Exam 1 on Statistics Applied to Natural Sciences | MATH 338 and more Exams Mathematics in PDF only on Docsity! Math- 338: Solutions for Part 2 of Exam 1, Monday March 9, 2009 To receive full credit you need to show detailed work. In other words, it is not sufficient to write the probability for some problem is 1.00!. You have 70 Minutes. (1) Easy! > z=c(1,2,3,4,5,6) > u=sample(z,size=1000000,prob=c(0.2,0.2,0.2,0.2,0.1,0.1),replace=T) > length(u[u==1]) [1] 199415 > length(u[u==2]) [1] 199886 > length(u[u==3]) [1] 200005 > length(u[u==4]) [1] 200424 > length(u[u==5]) [1] 100336 > length(u[u==6]) [1] 99934 (2) > u1=rbinom(100000,450,1/3) > u2=rnorm(100000,150,10) First, we need to find out what are the cut-off values associated with 1, 2, and 3 standard deviations away from the mean. Then we need to calculate the associated areas for the vectors of simulated values (u1, and u2). > u1=rbinom(100000,450,1/3) > u2=rnorm(100000,150,10) > length(u1[u1>=140&u1<=160])/100000 [1] 0.70456 > length(u2[u2>=139.5&u2<=160.5])/100000 [1] 0.70397 > length(u1[u1>=130&u1<=170])/100000 [1] 0.9596 > length(u2[u2>=129.5&u2<=170.5])/100000 1