(a) A type of lightbulb is labeled as having an average lifetime of 1000 hours. It's reasonable to model the probability of failure of these bulbs by an exponential density function with mean u 1000 (i) Use this model to find the probability that a bulb fails within the first 300 hours. (Round your answer to three decimal places.) (ii) Use this model to find the probability that a bulb burns for more than 700 hours. (Round your answer to three decimal places.) (b) What is the median lifetime of these lightbulbs? (Round your answer to one decimal place.) hr According to the National Health Survey, the heights adult males in the United States are normally distributed with mean 69.0 inches and standard deviation 2.8 inches. (a) What is the probability that an adult male chosen at random is between 67 and 71 inches tall? (Round your answer to three decimal places.) (b) What percentage of the adult male population is more than 6 feet tall? (Round your answer to one decimal place.)

(a) A type of lightbulb is labeled as having an average lifetime of 1000 hours. It's reasonable to model the probability of failure of these bulbs by an exponential density function with mean u 1000 (i) Use this model to find the probability that a bulb fails within the first 300 hours. (Round your answer to three decimal places.) (ii) Use this model to find the probability that a bulb burns for more than 700 hours. (Round your answer to three decimal places.) (b) What is the median lifetime of these lightbulbs? (Round your answer to one decimal place.) hr According to the National Health Survey, the heights adult males in the United States are normally distributed with mean 69.0 inches and standard deviation 2.8 inches. (a) What is the probability that an adult male chosen at random is between 67 and 71 inches tall? (Round your answer to three decimal places.) (b) What percentage of the adult male population is more than 6 feet tall? (Round your answer to one decimal place.)

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Description: Answer the 2 parts of the question attached as images. (a) A type of lightbulb is labeled as having an average lifetime of 1000 hours. It's reasonable to model the probability of failure of these bulbs by an exponential density function with mean u 1

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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(a) A lamp has two bulbs, each of a type with average lifetime 1800 hours. Assuming that we can model the probability of failure of these bulbs by an exponential density function with mean μ = 1800, find the probability that both of the lamp's bulbs fail within 1800 hours. (Round your answer to four decimal places.)(b) Another lamp has just one bulb of the same type as in part (a). If one bulb burns out and is replaced by a bulb of the same type, find the probability that the two bulbs fail within a total of 1800 hours. (Round your answer to four decimal places.)
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(a) A lamp has two bulbs, each of a type with average lifetime 1300 hours. Assuming that we can model the probability of failure of these bulbs by an exponential density function with mean ? = 1300, find the probability that both of the lamp's bulbs fail within 1500 hours. (Round your answer to four decimal places.) (b) Another lamp has just one bulb of the same type as in part (a). If one bulb burns out and is replaced by a bulb of the same type, find the probability that the two bulbs fail within a total of 1500 hours. (Round your answer to four decimal places.)