Assume that the average talk time on an Apple iPhone is 20 hours and that this time follows the exponential probability distribution. What is the probability that a randomly selected iPhone will experience between 10 and 30 hours of talk time?

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Quizplus · Accepted Answer

The exponential distribution is given by the formula $P(X \leq x) = 1 - e^{-\lambda x}$, where $\lambda = \frac{1}{\text{mean}} = \frac{1}{20}$. To find the probability that a randomly selected iPhone will experience between 10 and 30 hours of talk time, we calculate $P(10 < X < 30)$. This is found by subtracting the probability that X is less than 10 from the probability that X is less than 30: $P(X < 30) - P(X < 10)$. Plugging in the values gives $1 - e^{-\frac{30}{20}} - (1 - e^{-\frac{10}{20}}) = e^{-0.5} - e^{-1.5}$, which calculates to approximately 0.3834.

Assume That the Average Talk Time on an Apple IPhone