A poll of 10 voters is taken in a large city. Let X be the number of voters in favor of candidate A for mayor. Suppose that 60% of all the city's voters favor this candidate. The mean and standard deviation are closest to

To find the mean and standard deviation for this situation, we can use the concept of a binomial distribution.

In this case, we have a binomial distribution because we are interested in the number of voters out of a fixed number of trials (in this case, the 10 voters in the poll) who favor candidate A. The probability of success (a voter favoring candidate A) is 0.60, and the probability of failure (a voter not favoring candidate A) is 0.40.

The mean (μ) of a binomial distribution is given by the formula μ = n * p, where n is the number of trials and p is the probability of success. In this case, n = 10 and p = 0.60. Therefore, the mean is μ = 10 * 0.60 = 6 voters.

The standard deviation (σ) of a binomial distribution is given by the formula σ = sqrt(n * p * q), where q is the probability of failure. In this case, q = 0.40. Therefore, the standard deviation is σ = sqrt(10 * 0.60 * 0.40) = sqrt(2.4) ≈ 1.55 voters.

So, the mean and standard deviation are closest to 6 voters and 1.55 voters, respectively.