Question

In October 2012, Apple introduced a much smaller variant of the Apple iPad, known as the iPad Mini. weighing less than 11 ounces, it was about 50% lighter than the standard iPad. Battery tests for the iPad Mini showed a mean life of 10.25 hours (the Wall Street Journal, October 31, 2012). Assume that battery life of the iPad Mini is uniformly distributed between 8.5 and 12 hours. a. Give a mathematical expression for the probability density function of battery life. b. what is the probability that the battery life for an iPad Mini will be 10 hours or less

Answer 1

Answer:

$\displaystyle P(8.5\leq x\leq 10)=0.56$

Step-by-step explanation:

Uniform Distribution

The probability density function PDF of the continuous uniform distribution is:

$p(x)={\begin{cases}{\frac {1}{b-a}}&\mathrm {for} \ a\leq x\leq b,\\[8pt]0&\mathrm {for} \ xb\end{cases}}$

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:

$p(x)={\begin{cases}{\frac {1}{4.5}}&\mathrm {for} \ 8.5\leq x\leq 12,\\[8pt]0&\mathrm {for} \ x12\end{cases}}$

b. We will find the probability that the battery life for an iPad Mini will be 10 hours or less, that is, $P(8.5\leq x\leq 10)$

The required probability is computed by using the upper part of the PDF, i.e.

$\displaystyle P(8.5\leq x\leq 10)=(10-8.5)\cdot \frac{1}{4.5}=0.56$

$\boxed{\displaystyle P(8.5\leq x\leq 10)=0.56}$