for the following problem, you will need the formulas below.\nthe mean/expected value of a discrete…

for the following problem, you will need the formulas below.\nthe mean/expected value of a discrete probability distribution is:\n\\(\\mu = \\sum x\\cdot p(x)\\).\nthe standard deviation of a discrete probability distribution is:\n\\(\\sigma = \\sqrt{\\sum x^{2}\\cdot p(x)-\\mu^{2}}\\).\nfor 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.\nenter the missing probability below, rounded to 3 significant figures.\n|x|p(x)|\n|0|0.468|\n|1|0.391|\n|2||\n|3|0.017|\n|4|0.001|\ncheck part answer

for the following problem, you will need the formulas below.\nthe mean/expected value of a discrete probability distribution is:\n\\(\\mu = \\sum x\\cdot p(x)\\).\nthe standard deviation of a discrete probability distribution is:\n\\(\\sigma = \\sqrt{\\sum x^{2}\\cdot p(x)-\\mu^{2}}\\).\nfor 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.\nenter the missing probability below, rounded to 3 significant figures.\n|x|p(x)|\n|0|0.468|\n|1|0.391|\n|2||\n|3|0.017|\n|4|0.001|\ncheck part answer

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:

$0.123$