Question

Suppose that 75% of Barcelona fans attended Barcelona vs Real Madrid football match played last Sunday live in the city and 25% live in the suburbs. If 12000 Barcelona fans were at the stadium, find the approximate probability that the number of fans from suburbs was fewer than 2900.

Answer 1

Sol:

p=0.25

n=12000

p^=x/n=2900/12000=0.2416667

sample follows normal distribution with mean=p^=0.25 and sample standard deviation is

sd=sqrt(p^*(1-p^)/n)=sqrt(0.25*(1-0.25)/12000)= 0.003952847

need to find

P(p^<0.2416667)

P(Z<p^-p/sqrt(p*(1-p)/n)

P(Z<-2.1082)

=0.0175

T he approximate probability that the number of fans from suburbs was fewer than 2900 is 0.0175