Question

suppose that the New England Colonials baseball team is equally likely to win any particular game as not to win it. 5 uppose also that we chocse a random sample of 30 Colonials games. Answer the following. (at necessary, consult a list of formulas.) (a) Estimate the number of games in the sample that the colonials win by giving the mean of the relevant distribution (that is, the expectation of the relevant random variable). Do not round your response. (b) Quantify the uncertainty of your estimate by giving the standard deviation of the distribution, Round your resporise to at least three decimal places.

Answer 1

To estimate the number of games won by the New England Colonials, calculate the mean of the binomial distribution (15 games), and for uncertainty, compute the standard deviation (approximately 2.739 when rounded).

Step-by-step explanation:

The question is asking us to use the principles of probability to answer questions related to the New England Colonials baseball team's game outcomes. Assuming the team has a 50% chance of winning any particular game and considering a sample of 30 games:

1. To estimate the number of games won in the sample, we calculate the mean of the binomial distribution, which is the product of the number of trials (n) and the probability of success (p). In this case, Mean (μ) = n * p = 30 * 0.5 = 15 games.
2. To quantify the uncertainty of the estimate, we calculate the standard deviation of the binomial distribution, which is given by the square root of the product of the number of trials (n), the probability of success (p), and the probability of failure (q). Thus, Standard Deviation (σ) = sqrt(n * p * q) = sqrt(30 * 0.5 * 0.5) ≈ 2.738613, when rounded to three decimal places.

These calculations help us understand the expected outcomes and variability for the Colonials' games based on probability theory.