Question

In a recent election 55% of people supported reelecting the incumbent. suppose a poll is done of 1440 people. if we used the normal as an approximation to the binomial, what would the mean and standard deviation be?

mean:
standard deviation:

Answer 1

To approximate the binomial distribution with the normal distribution, the mean of the normal distribution is calculated by multiplying the proportion of people supporting the incumbent by the total number of people polled. The standard deviation of the normal distribution is calculated using the formula sqrt(n * p * (1 - p)).

Step-by-step explanation:

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

Given that 55% of people supported reelecting the incumbent, the mean of the binomial distribution is 0.55 multiplied by the total number of people polled (1440). So, the mean of the normal distribution would be 0.55 * 1440 = 792.

The standard deviation of the binomial distribution can be calculated using the formula: sqrt(n * p * (1 - p)), where n is the total number of people polled and p is the proportion of people supporting the incumbent (0.55). So, the standard deviation of the normal distribution would be sqrt(1440 * 0.55 * (1 - 0.55)) = 16.17 (approx).

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