Q49E The next presidential election. ... [FREE SOLUTION]

91影视

Statistics For Business And Economics

James T. McClave, P. George Benson, Terry Sincich

$Math Studyset 91影视 Explanations$ Math

13th Edition 路 888 pages

ISBN: 9780134506593

Chapter 4: Q49E (page 239)

The next presidential election. A recent study suggested that 70% of all eligible voters will vote in the next presidential election. Suppose 20 eligible voters are randomly selected from the population of all eligible voters.
a. Analyze the potential outcomes for the sample using the binomial random variable.
b. Use a binomial probability table to find the probability that more than 12 of the eligible voters sampled will vote in the next presidential election.
c. Use a binomial probability table to find the probability that more than 10 but fewer than 16 of the 20 eligible voters sampled will vote in the next presidential election.

Short Answer

Expert verified

A binomial random variable can have any number between 0 as well as n.
$P (X 猢� 12) = 0.772$
$P (16 猢� X 猢� 20) = 0.714$

Step by step solution

Given information

70% of all eligible voters will vote in the next presidential election

n=20

(a)Finding potential outcomes

The experiment comprises of n similar as well as independent trials, with n predetermined. Every trial can have one of two results: success (S) as well as failures (F), with the likelihood of succeeding (p) being equal from trial to trial. A binomial random variable can have any number between 0 as well as n.

(b) Finding the probability that more than 12 of the eligible voters sampled will vote in the next presidential election

$\begin{array}{rcl} P (X 猢� 12) & = & P (X = 12) + P (X = 13) + . . . + P (X = 20) \\ = & {鈭�}_{i = 12}^{20} (\begin{matrix} 20 \\ i \end{matrix}) p^{i} {(1 - p)}^{20 - i} \\ = & 0.772 \end{array}$

Thus, the required probability is 0.772.

(c) Finding the probability that more than 10 but fewer than 16 of the 20 eligible voters sampled will vote in the next presidential election

$\begin{array}{rcl} P (16 猢� X 猢� 20) & = & P (X = 16) + P (X = 17) + . . . + P (X = 20) \\ = & {鈭�}_{i = 16}^{20} (\begin{matrix} 20 \\ i \end{matrix}) p^{i} {(1 - p)}^{20 - i} \\ = & 0.714 \end{array}$