Answer:
[tex]\displaystyle P(8.5\leq x\leq 10)=0.56[/tex]
Step-by-step explanation:
Uniform Distribution
The probability density function PDF of the continuous uniform distribution is:
[tex]p(x)={\begin{cases}{\frac {1}{b-a}}&\mathrm {for} \ a\leq x\leq b,\\[8pt]0&\mathrm {for} \ x<a\ \mathrm {or} \ x>b\end{cases}}[/tex]
Where a and b are the lower and upper limits where the probabilities are defined.
a. For our problem a=8.5, b=12, thus b-a=4.5 and the PDF is:
[tex]p(x)={\begin{cases}{\frac {1}{4.5}}&\mathrm {for} \ 8.5\leq x\leq 12,\\[8pt]0&\mathrm {for} \ x<8.5\ \mathrm {or} \ x>12\end{cases}}[/tex]
b. We will find the probability that the battery life for an iPad Mini will be 10 hours or less, that is, [tex]P(8.5\leq x\leq 10)[/tex]
The required probability is computed by using the upper part of the PDF, i.e.
[tex]\displaystyle P(8.5\leq x\leq 10)=(10-8.5)\cdot \frac{1}{4.5}=0.56[/tex]
[tex]\boxed{\displaystyle P(8.5\leq x\leq 10)=0.56}[/tex]
