In October 2012, Apple introduced a much smaller variant of the Apple iPad, known as theiPad 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 between8.5 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?c. what is the probability that the battery life for an iPad Mini will be at least 11 hours?d. what is the probability that the battery life for an iPad Mini will be between 9.5 and11.5 hours?e. In a shipment of 100 iPad Minis, how many should have a battery life of at least9 hours?
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
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
b. what is the probability that the battery life for an iPad Mini will be 10 hours or less?
c. what is the probability that the battery life for an iPad Mini will be at least 11 hours?
d. what is the probability that the battery life for an iPad Mini will be between 9.5 and
11.5 hours?
e. In a shipment of 100 iPad Minis, how many should have a battery life of at least
9 hours?
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