Question

The Ents are marching to Isengard. Each Ent's marching speed is uniformly dis- tributed between 1 and 5 miles per hour. There are currently 50 Ents in the group Pippin would like to know the probability that their average speed is greater than 3.25 miles per hour

Answer 1

here for uniform distribution parameter a =1 and b=5

therefore mean =(a+b)/2=(1+5)/2=3

and std deviation =(b-a)/sqrt(12)=(5-1)/sqrt(12)=1.1547

for 50 Ents ; estimated sample mean =3

and std error of mean =std deviation/sqrt(50)=1.1547/sqrt(50)=0.163

hence from normal approximation ; P(average speed is greater then 3.25 miles per hour)=P(Xbar>3.25)

=1-P(Xbar<3.25)=1-P(Z<(3.25-3)/0.163)=1-P(Z<1.53)=1-0.9370 =0.0630