Question

g in october 2012, apple introduced a much smaller version of the apple ipad, known as the ipad mini. weighing less than 11 ounces, it was 50% lighter than the standard ipad. battery tests for the mini ipad showed that battery life is uniformly distributed between 8.5 and 12 hours. calculate the expected value to two decimals.

Answer 1

Using the concepts of probability, we got that 0.4286 is the probability  that the battery life for an iPad Mini will be 10 hours or less  which is about 42.86%.

From the given information;

Let  X represent the continuous random variable with uniform distribution U (A, B) . Therefore the probability density function can now be determined as :

$f_X(x)$ = $\frac{1}{B-A}$ where A<x<B

where A and B  are the two parameters of the uniform distribution

From the question;

Assume that battery life of the iPad Mini is uniformly distributed between 8.5 and 12 hours

So; Let A = 8,5 and B = 12

Therefore; the mathematical expression for the probability density function of battery life is :

$f_X(x)$ = [1 / (12-8.5)]8.5<x<12

$f_X(x)=$(1/3.5)8.5<x<12

The  probability that the battery life for an iPad Mini will be 10 hours or less can be calculated as:

F(x) = P(X ≤x)

F(10)=$(x-A)/(B-A)$

F(10)=(10-8.5)/(12-8.5)

F(10)=1.5/3.5

F(10)=0.4286

Hence, the probability that the battery life for an iPad Mini will be 10 hours or less is 0.4286

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(Complete question)

In October of 2012, Apple introduced a much smaller variant of the Apple iPad, known at 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. What is the probability that the battery life for an iPad Mini will be 10 hours or less (to 4 decimals)?