Question

Suppose that 44​% of all adult Australians believe that Australia should become a republic. Calculate the probability that more than 47​% of a random sample of 150 adult Australians would believe this.

Answer 1

Here we assume that  44% of adult Australians believe that Australia should apply to host the next rugby World Cup.

Let P = 0.44

And we want to find the probability that more than 47% of a random sample of 150 adult Australians would believe this.

Mathematically,  

P( P > 0.47) = 1 - P( P < 0.47) ....( 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 = 0.44

Standard deviation =

Let's use excel:

P( P < 0.47) = "=NORMDIST(0.47,0.44,0.04053,1)" = 0.7704

Plug this value in equation ( 1 ), we get

P( P > 0.47) = 1 -  0.7704 = 0.2296 ( This is the final answer

#the probability that more than 47​% of a random sample of 150 adult is 0.2296