Question

In a recent election 56% of people supported reelecting the incumbent. suppose a poll is done of 1250 people.

If we used the normal as an approximation to the binomial, what would the mean and standard deviation be?

Answer 1

The mean of the distribution for the reelection support poll would be 700, and the standard deviation would be approximately 16.437.

Step-by-step explanation:

When using the normal approximation to the binomial distribution in the context of a poll predicting incumbent reelection, we find the mean (expected value) and standard deviation of the distribution based on the number of trials and the probability of success for each trial.

Given that 56% of people supported reelection and the poll sampled 1250 people, the mean would be calculated as the product of the number of trials and the probability of success, hence 700 (1250 * 0.56).

The standard deviation is found using the formula for the standard deviation of a binomial distribution, which involves the number of trials, the probability of success, and the probability of failure (1 - probability of success); therefore, it would be approximately 16.437 (sqrt(1250 * 0.56 * 0.44)).