Question

A company introduced a much smaller variant of its tablet, known as the tablet junior. Weighing less than 11 ounces, it was about 50% lighter than the standard tablet. Battery tests for the tablet junior showed a mean life of 9.75 hours. Assume that battery life of the tablet junior is uniformly distributed between 7.5 and 12 hours.
a. Give a mathematical expression for the probablility density function of battery life.
b. What is the probablility that the battery life for the tablet junior will be 9.5 hours or less?

Answer 1

Answer:

a) $f(x) = \left \{ {{\frac{1}{4.5}, a \leq x \leq b} \atop {0, \text{otherwise}}} \right$

b) 44.44% probablility that the battery life for the tablet junior will be 9.5 hours or less

Step-by-step explanation:

An uniform probability is a case of probability in which each outcome is equally as likely.

For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.

The uniform probability distribution has the following density function:

$f(x) = \left \{ {{\frac{1}{b-a}, a \leq x \leq b} \atop {0, \text{otherwise}}} \right$

The probability that we find a value X lower than x is given by the following formula.

$P(X \leq x) = \frac{x - a}{b-a}$

a)

Assume that battery life of the tablet junior is uniformly distributed between 7.5 and 12 hours.

This means that $a = 7.5, b = 12$

$f(x) = \left \{ {{\frac{1}{12 - 7.5}, a \leq x \leq b} \atop {0, \text{otherwise}}} \right$

$f(x) = \left \{ {{\frac{1}{4.5}, a \leq x \leq b} \atop {0, \text{otherwise}}} \right$

b)

$P(X \leq x) = \frac{x - a}{b-a}$

$P(X \leq 9.5) = \frac{9.5 - 7.5}{12 - 7.5} = 0.4444$

44.44% probablility that the battery life for the tablet junior will be 9.5 hours or less