Question

determine the required value of the missing probability to make the distribution a discrete probability distribution. p(4)= (type an integer or a decimal.)

Explanation:

Step1: Recall the property of discrete probability distribution

The sum of all probabilities in a discrete probability distribution is \(1\). Let \(P(4) = p\). Then \(P(3)+P(4)+P(5)+P(6)=1\).

Step2: Substitute the known values

We know that \(P(3) = 0.19\), \(P(5)=0.48\), \(P(6) = 0.09\). Substituting into the equation \(0.19 + p+0.48 + 0.09=1\).

Step3: Simplify the left - hand side of the equation

First, add the known probabilities: \(0.19+0.48 + 0.09=\frac{19 + 48+9}{100}=\frac{76}{100}=0.76\). So the equation becomes \(p+0.76 = 1\).

Step4: Solve for \(p\)

Subtract \(0.76\) from both sides of the equation: \(p=1 - 0.76\).

Answer:

\(0.24\)