Question

In October 2012, Apple introduced a much smaller variant of the Apple iPad, known as the iPad Mini. Weighing less than 1 1 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 c) What is the probability that the battery life for an iPad Mini will be at least 11 d) What is the probability that the battery life for an iPad Mini will be between 9.5 e) In a shipment of 100 iPad Minis, how many should have a battery life of at less? hours? and 11.5 hours? least 9 hours?

Answer 1

(a)

Mathematical expression for the probability density function of battery life is given by:

for 8.5 X 12

=0,

otherwise

(b)

$=rac{2}{7}x$

between limits 8.5 to 10

Applying limits, we get:

P(X < 10) “ × 1.5= 0.4286

So,

Answer is:

0.4286

(c)

$=rac{2}{7}x$

between limits 11 to 12

Applying limits, we get:

P(X > 11) =-× (12-11) 0.2857

So,

Answer is:

0.2857

(d)

$=rac{2}{7}x$

between limits 9.5 to 11.5

Applying limits, we get:

So,

Answer is:

0.5714

(e)

$=rac{2}{7}x$

between limits 9 to 12

Applying limits, we get:

So,

Number of iPad Minis = 0.8571 X 100 = 86

Answer is:

86