Question

Suppose that 50% of adult Australians believe that Australia should apply to host the next rugby World Cup. Calculate the probability that more than 56% of a random sample of 150 adult Australians would believe this.

Answer 1

Here we assume that  50% of adult Australians believe that Australia should apply to host the next rugby World Cup.

Let P = 0.50

And we want to find the probability that more than 56% of a random sample of 150 adult Australians would believe this.

Mathematically,  

P( P > 0.56) = 1 - P( P < 0.56) ....( 1 )

Here n = 150 which is very large and we can use normal approximation to find the probability.

The mean and standard deviation of sample proportion are as follows.

mean = = P = 0.50

Standard deviation =

Let's use excel:

P( P < 0.56) = "=NORMDIST(0.56,0.5,0.040825,1)" = 0.929177

Plug this value in equation ( 1 ), we get

P( P > 0.56) = 1 -  0.929177 = 0.070823 ( This is the final answer).