Question

question number 1. (10.00 points) given the following sampling distribution: what is p(x = 15)? o 0.84 o 0.83 o 0.15 o 0.82 o 0.85 o none of the above

Explanation:

Step1: Recall probability - distribution property

In a probability - distribution, the sum of all probabilities $P(X)$ for all possible values of $X$ is 1. First, find the sum of the given probabilities.
The given probabilities for $X=-20,\ -14,\ -2,\ 12$ are $P(-20)=\frac{1}{50}$, $P(-14)=\frac{3}{50}$, $P(-2)=\frac{1}{25}$, $P(12)=\frac{1}{25}$.
Convert the fractions to a common denominator. $\frac{1}{25}=\frac{2}{50}$.
The sum of the given probabilities is $\frac{1 + 3+2 + 2}{50}=\frac{8}{50}=0.16$.

Step2: Calculate $P(X = 15)$

Let $P(X = 15)=p$. Since the sum of all probabilities in a probability - distribution is 1, we have $0.16 + p=1$.
Solve for $p$: $p=1 - 0.16=0.84$.

Answer:

0.84