use the probability distribution graph to answer the question. $p(xleq a)=0.75$ what is the value of a…

Explanation:

Step1: Analyze the probability graph

We know that $P(X\leq a)=0.75$. Looking at the graph, the probability is uniformly - distributed over the interval from $x = 1$ to $x = 5$ with a height of $0.25$.

Step2: Calculate the cumulative probability

The area of the rectangle from $x = 1$ to $x = 5$ is $A=(5 - 1)\times0.25=1$. We want to find the value of $a$ such that the cumulative probability up to $a$ is $0.75$. The base of the rectangle for the cumulative probability starts at $x = 1$. Let the upper - bound be $a$. The area of the rectangle representing the cumulative probability is $A=(a - 1)\times0.25$.

Step3: Solve for $a$

Set $(a - 1)\times0.25=0.75$. Divide both sides by $0.25$: $\frac{a - 1}{1}=\frac{0.75}{0.25}=3$. Then add $1$ to both sides: $a=3 + 1=4$.

Answer:

$4$