The sampling distribution of can be approximated as a Normal Distribution only if:
np and nq are both equal to or greater than 10. i.e.
np ≥ 10
nq ≥ 10
Both of these conditions must be met in order to approximate the sampling distribution of as Normal Distribution.
From the given data:
n = 50
p = 0.80
q = 1 - p = 1 - 0.80 = 0.20
np = 50(0.80) = 40
nq = 50(0.20) = 10
This means the conditions that np and nq must be equal to or greater than 10 is being satisfied. So, we can conclude that the sampling distribution of pˆ is approximately a normal distribution
Because england, scotland and france are european team and they make up 3/5 of all the teams, you multiply 3/5 by 2/5 because the south american teams are brazil and argentina which make up 2/5 of the total teams. So the probability that a european team will play a south american team is 3/5*2/5 which is 6/25
since the second figure is also a square, then the sides touching the diagonals have to be all equal, and that'd only happen if those sides bisects the larger square's diagonal.