Show all work. Answers given without the proper mathematical explanation will re
ID: 2924375 • Letter: S
Question
Show all work. Answers given without the proper mathematical explanation will receive little to no credit. You will also be graded on notation. 1. A small voting district has 101 female voters and 95 male voters. A random sample of 10 voters is drawn. Let the random variable X count the number of female votes in the sample of size ten. (a) What is the probability exactly 7 of the voters will be female? That is, find P(X = 7). lo! 10-7 .si .1261 .. )! (b) How many female votesr do we expect to obtain? That is, find E(X). (c) Find the variance of X, Var(X).Explanation / Answer
Probability is p=101/(101+95)=0.5153
N is 10
a) P(x=7) =10C7*(0.5153)^7*(1-0.5153)^3=0.1318
b) Expected value is N*p=10*0.5153 =5.153
c) Variance is N*p*(1-p)=10*0.5153*(1-0.5153)=2.4977
standard deviation is square root of variance , thus sqrt(2.4977)=1.58