Could you please explain how to do this question. Suppose that a certain candidate is running in a city election. A recent poll of 500 randomly chosen voters concludes that 60% of the voters prefer this candidate. Determine the probability that the candidate will get less than 56% of the votes.

To determine the probability that the candidate will get less than 56% of the votes, we can use the concept of the binomial distribution. The binomial distribution is used to model situations where there are only two possible outcomes (in this case, voters either prefer the candidate or they do not), and each outcome has a fixed probability of occurring (in this case, the probability of a voter preferring the candidate is 60%).

To calculate the probability, we need to find the cumulative probability of the candidate receiving less than 56% of the votes.

Step 1: Identify the relevant values:
- Number of trials (n): 500 (as stated in the question, the poll was conducted among 500 randomly chosen voters)
- Probability of success (p): 0.60 (60% of the voters prefer the candidate)
- Number of successes (x): Less than 56% of 500 votes, which can be calculated as 0.56 * 500 = 280 (approximately).

Step 2: Calculate the probability using the binomial distribution formula:
P(X < 280) = Σ (for x = 0 to 279) [C(n, x) * p^x * (1-p)^(n-x)]

In this formula, C(n, x) represents the combination or "choose" function, which calculates the number of ways to choose x successes out of n trials.

Step 3: Use statistical software or available tables to calculate the probability.
Using a statistical software or binomial tables, you can find the cumulative probability directly by inputting the values from Step 1 into the formula and summing up the probabilities for each value of x from 0 to 279.

Alternatively, you can also use Excel or other spreadsheet programs to calculate the probability by using the "BINOM.DIST" function. The function would be:

= BINOM.DIST(279, 500, 0.60, TRUE)

This formula will give you the probability of the candidate receiving less than 56% of the votes.