Math Problem Statement
Suppose that the average time a fully charged 6-volt laptop battery will operate a computer is 4.2 hours and follows the exponential probability distribution. Determine the following probabilities. a) Determine the probability that the next charge will last less than 2.3 hours. b) Determine the probability that the next charge will last between 2.3 and 3.3 hours. c) Determine the probability that the next charge will last more than 2.8 hours. Question content area bottom Part 1 a) The probability that the next charge will last less than 2.3 hours is enter your response here. (Round to four decimal places as needed.) Part 2 b) The probability that the next charge will last between 2.3 and 3.3 hours is enter your response here. (Round to four decimal places as needed.) Part 3 c) The probability that the next charge will last more than 2.8 hours is enter your response here. (Round to four decimal places as needed.)
Solution
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Math Problem Analysis
Mathematical Concepts
Exponential Probability Distribution
Probability
Cumulative Distribution Function (CDF)
Formulas
f(x; λ) = λe^{-λx}
F(x; λ) = 1 - e^{-λx}
P(a ≤ X ≤ b) = F(b; λ) - F(a; λ)
P(X > x) = e^{-λx}
Theorems
Exponential Distribution
Memoryless Property of Exponential Distribution
Suitable Grade Level
Grades 11-12 and College Level
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