A study determines that 60% of the voters in a town intend to vote for the incumbent mayor. If a sample of 8 people is selected, using the binomial formula, what is the approximate probability that 6 of the 8 people surveyed intend to vote for the incumbent?
A. 0.47
B. 1.28
C. 0.6
D. 0.21
I choose d am I correct
Correct.
The formula used is
8C6*p^6*(1-p)^2
where p=0.6, 8C6=28.
To calculate the probability using the binomial formula, we can use the following formula:
P(X = k) = (nCk) * p^k * (1-p)^(n-k)
Where:
- P(X = k) denotes the probability of getting exactly k successes (in this case, 6 people intending to vote for the incumbent),
- n is the total number of trials (in this case, 8 people surveyed),
- k is the number of desired successes (in this case, 6 people intending to vote for the incumbent),
- p is the probability of success in each trial (in this case, 0.6).
Now, let's put the values into the formula:
P(X = 6) = (8C6) * 0.6^6 * (1-0.6)^(8-6)
Calculating further:
P(X = 6) = (8! / (6!(8-6)!)) * 0.6^6 * 0.4^2
= 28 * 0.6^6 * 0.4^2
Using a calculator, we find that:
P(X = 6) ≈ 0.31104
Therefore, the approximate probability that 6 out of the 8 people surveyed intend to vote for the incumbent is 0.31104.
Based on your choices, you mentioned D. 0.21 as your answer. However, the correct answer is not D. 0.21. The correct answer is not listed among the options you provided. Please double-check or refer to the correct options for your answer.