Question

for the following problem, you will need the formulas below.
the mean/expected value of a discrete probability distribution is:
\\(\mu = \sum x\cdot p(x)\\).
the standard deviation of a discrete probability distribution is:
\\(\sigma = \sqrt{\sum x^{2}\cdot p(x)-\mu^{2}}\\).
for the entire world’s population, approximately 17.3% of all people speak chinese as their native language. suppose four people are randomly selected from the earth’s population, and define x to be the number of these who speak chinese as their native language. the probability distribution associated with this random variable is given below with one missing probability.
enter the missing probability below, rounded to 3 significant figures.

x	p(x)
0	0.468
1	0.391
2
3	0.017
4	0.001

check part answer

Explanation:

Step1: Recall probability - sum property

The sum of all probabilities in a probability distribution is 1. Let the missing probability be $P(2)$. Then $\sum_{x = 0}^{4}P(x)=1$.

Step2: Set up the equation

$P(0)+P(1)+P(2)+P(3)+P(4)=1$.
Substitute the known values: $0.468 + 0.391+P(2)+0.017 + 0.001=1$.

Step3: Solve for $P(2)$

First, add the known - value probabilities: $0.468+0.391 + 0.017+0.001=0.877$.
Then, $P(2)=1 - 0.877$.
$P(2)=0.123$.

Answer:

$0.123$