We are given the following uniform distribution:
The probability that the absolute value of the number is in the following interval:
[tex]\begin{gathered} -7The probability is the area under the curve of the distribution. Therefore, we need to add both areas. The height of the distribution is:[tex]H=\frac{1}{b-a}[/tex]Where:
[tex]\begin{gathered} a=-7 \\ b=7 \end{gathered}[/tex]Substituting we get:
[tex]H=\frac{1}{7-(-7)}=\frac{1}{14}[/tex]Therefore, the areas are:
[tex]P(\lvert x\rvert>1.5)=(-1.5-(-7))(\frac{1}{14})+(7-1.5)(\frac{1}{14})[/tex]Simplifying we get:
[tex]P(\lvert x\rvert>1.5)=2(7-1.5)(\frac{1}{14})[/tex]Solving the operations:
[tex]P(\lvert x\rvert>1.5)=0.7857[/tex]Therefore, the probability is 0.7857 or 78.57%.
