Question

use the normal distribution to approximate the following binomial distribution. you claim that 73% of the voters in your district will vote for you. if the district has 350 voters, what is the probability that at least 273 will actually vote for you?

Answer 1

To approximate the binomial distribution using the normal distribution, we can use the mean and standard deviation of the binomial distribution to calculate the mean and standard deviation of the normal distribution. In this case, the probability that at least 273 voters will vote for you is approximately 0.9798.

Step-by-step explanation:

To approximate the binomial distribution using the normal distribution, we can use the mean and standard deviation of the binomial distribution to calculate the mean and standard deviation of the normal distribution.

In this case, the binomial distribution has n = 350 (number of voters) and p = 0.73 (probability of voting for you), so the mean of the binomial distribution is given by np = 350*0.73 = 255.5 and the standard deviation is given by sqrt(np(1-p)) = sqrt(350*0.73*(1-0.73))

= 8.54.

Now, using the normal distribution, we can calculate the z-score for the desired value of at least 273 votes: z = (x - mean) / standard deviation = (273 - 255.5) / 8.54

= 2.04.

Finally, we can use the z-score to find the probability associated with it. We can refer to a standard normal distribution table or use a calculator to find that the probability for a z-score of 2.04 is approximately 0.9798.

So, the probability that at least 273 voters will vote for you is approximately 0.9798.