The federal government states that 85% of Canadians are in favor of Canada\'s ra

Question

The federal government states that 85% of Canadians are in favor of Canada's ratifying the Kyoto Accord if this is the true proportion of Albertans favoring ratification, (input answers to four decimal places) what is the probability that, in a random sample of 40 Albertans, exactly 24 would support ratification? !! middot what is the probability that at least 24 but no more than 34 would support ratification? ill what is the expected number in a sample of 40 Albertans who would oppose ratification?

Explanation / Answer

Binomial Distribution
PMF of B.D is = f ( k ) = ( n k ) p^k * ( 1- p) ^ n-k
Where   
k = number of successes in trials
n = is the number of independent trials
p = probability of success on each trial
a.
P( X = 24 ) = ( 40 24 ) * ( 0.85^24) * ( 1 - 0.85 )^16
= 0.0001
b.
Normal Approximation to Binomial Distribution
Mean ( np ) =40 * 0.85 = 34
Standard Deviation ( npq )= 40*0.85*0.15 = 2.2583
Normal Distribution = Z= X- u / sd                   
To find P(a < = Z < = b) = F(b) - F(a)
P(X < 24) = (24-34)/2.2583
= -10/2.2583 = -4.4281
= P ( Z <-4.4281) From Standard Normal Table
= 0
P(X < 34) = (34-34)/2.2583
= 0/2.2583 = 0
= P ( Z <0) From Standard Normal Table
= 0.5
P(24 < X < 34) = 0.5-0 = 0.5                  
c.
Mean ( np ) =40 * 0.85 = 34

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