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 abo

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

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Bella 2 weeks 2021-09-15T01:29:04+00:00 1 Answer 0

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    2021-09-15T01:30:45+00:00

    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} \ x<a\ \mathrm {or} \ x>b\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} \ x<8.5\ \mathrm {or} \ x>12\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}

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