Question

mixed knowledge check question 23 suppose that the new england colonials baseball team is equally likely to win any particular game as not to win it. suppose also that we choose a random sample of 30 colonials games. answer the following. (if 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. 25 (b) quantify the uncertainty of your estimate by giving the standard deviation of the distribution. round your response to at least three decimal places. 3.536

Explanation:

Step1: Identify distribution parameters

This is a binomial distribution with $n=30$ (number of trials) and $p=0.5$ (probability of success/win).

Step2: Calculate the mean (part a)

The mean of a binomial distribution is $\mu = np$.
$\mu = 30 \times 0.5 = 15$

Step3: Calculate standard deviation (part b)

The standard deviation of a binomial distribution is $\sigma = \sqrt{np(1-p)}$.
$\sigma = \sqrt{30 \times 0.5 \times (1-0.5)} = \sqrt{7.5} \approx 2.7386$

Answer:

(a) 15
(b) 2.739