### Exponential Distribution and Lightbulb LifetimesA type of lightbulb is labeled as having an average lifetime of 1,000 hours. It is reasonable to model the probability of failure of these bulbs using an exponential density function with a mean (μ) of 1,000 hours.#### Tasks:**(a)** 1. **Find the Probability of Early Failure:** - Use this model to find the probability that a bulb fails within the first 400 hours. - **Note:** Round your answer to three decimal places. - **Input Required:** Enter a number.2. **Find the Probability of Extended Use:** - Use this model to find the probability that a bulb burns for more than 600 hours. - **Note:** Round your answer to three decimal places. - **Input Required:** Enter a number (currently indicated with a red "X").**(b)** - **Determine the Median Lifetime:** - Calculate the median lifetime of these lightbulbs. - **Note:** Round your answer to one decimal place. - **Answer:** 693.2 hours (indicated with a green checkmark).This exercise involves statistical modeling and understanding exponential distribution for predicting the failure rates of products.

(a) A type of lightbulb is labeled as having an average lifetime of 1,000 hours. It's reasonable to model the probability of failure of these bulbs by an exponential density function with mean = 1,000. (i) Use this model to find the probability that a bulb fails within the first 400 hours. (Round your answer to three decimal places.) Enter a number. 4 (ii) Use this model to find the probability that a bulb burns for more than 600 hours. (Round your answer to three decimal places.) x (b) What is the median lifetime of these lightbulbs? (Round your answer to one decimal place.) 693.15 ✓hr

(a) A type of lightbulb is labeled as having an average lifetime of 1,000 hours. It's reasonable to model the probability of failure of these bulbs by an exponential density function with mean = 1,000. (i) Use this model to find the probability that a bulb fails within the first 400 hours. (Round your answer to three decimal places.) Enter a number. 4 (ii) Use this model to find the probability that a bulb burns for more than 600 hours. (Round your answer to three decimal places.) x (b) What is the median lifetime of these lightbulbs? (Round your answer to one decimal place.) 693.15 ✓hr

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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