Question

given the following sampling distribution: what is p(x = 15)? 0.84 0.15 0.85 0.83 0.86 none of the above

Explanation:

Step1: Recall probability - distribution property

The sum of all probabilities in a probability - distribution is 1. Let \(P(X = 15)=p\).
We have the probabilities \(\frac{3}{100}=0.03\), \(\frac{1}{20}=0.05\), \(\frac{1}{25}=0.04\), \(\frac{1}{25}=0.04\) for \(X=-18\), \(X = - 14\), \(X=-2\), \(X = 4\) respectively.

Step2: Set up equation

\(0.03+0.05 + 0.04+0.04+p=1\).

Step3: Simplify left - hand side

\((0.03 + 0.05)+(0.04 + 0.04)+p=1\), \(0.08+0.08 + p=1\), \(0.16+p=1\).

Step4: Solve for \(p\)

\(p=1 - 0.16=0.84\).

Answer:

0.84