Question

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. 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 response to at least three decimal places. (If necessary, consult a list of formulas.) a. | b. 1 Х 5 ?

Answer 1

Here given that the New England Colonials baseball team is equally likely to win any particular game as not to win it.

So, probability of win in any game is 0.5, (i.e,p=0.5)

Let define a random variable X that represent number of ges win New England Colonials games.

Here we choose a random sample of 30 colonials games.

So, the random variable X follow binomial distribution with parameters n=30 and p=0.5

$i.e, X\sim Binomial (n=30,p=0.5)$

(a) We need to find the expected value of X.

Solution::

We know that X follow binomial distribution,

So, the expected value is given by,

$\therefore E(X)=np=30\times 0.5=15$

The expected or mean value is 15

(b) We need to find the standard deviation of X

Solution::

We know that X that binomial distribution,

So, the standard deviation is given by,

$\therefore Stdv(X)=\sqrt{Var(X)}=\sqrt{np(1-p)}=\sqrt{30\times 0.5\times (1-0.5)}$

$\therefore Stdv(X)=\sqrt{30\times 0.5\times 0.5}$

1. Stdv (X) = V7.5

$\therefore Stdv(X)=2.73861279$

$\therefore Stdv(X)\simeq 2.739$[ round to three decimal place]

The standard deviation is 2.739