Question

76​% of U.S. adults think that political correctness is a problem in America today. You randomly select six U.S. adults and ask them whether they think that political correctness is a problem in America today. The random variable represents the number of U.S. adults who think that political correctness is a problem in America today. Answer the questions below.

Answer 1

Answer:

$E(x) = 4.56$ --- Mean

$s^2 = 1.0944$ --- Variance

$s = 1.0461$ --- Standard Deviation

Step-by-step explanation:

See Comment for missing details

Given

$p = 0.76$ --- proportion

$n = 6$ -- sample

Solving (a): The mean; E(x)

This is calculated as:

$E(x) = n * p$

Substitute values for n and p

$E(x) = 6 * 0.76$

$E(x) = 4.56$

Solving (b): The variance; s^2

This is calculated as:

$s^2 = n*p*(1-p)$

Substitute values for n and p

$s^2 = 6 * 0.76 * (1-0.76)$

$s^2 = 6 * 0.76 * 0.24$

$s^2 = 1.0944$

Solving (c): The standard deviation; s

This is calculated as:

$s = \sqrt{s^2$

Substitute value for s^2

$s = \sqrt{1.0944$

$s = 1.0461$