### 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...

See similar textbooks

Similar questions

Scenario: A researcher wants to determine whether the volume of orders placed, in thousands, can predict whether an entry error was committed (yes or no). Which research analysis is most appropriate? Group of answer choices a. ANOVA b. Binary Logistic Regression c. Chi-square Contingency Table d. Non-parametric e. Regression
5
I only need B,C, and D
Q.4. Annual depth of precipitation X (cm) is assumed to be lognormally distributed with u-50, o=10. What is the probability of the precipitation to remain in the range of 45 and 62 cm?
3
probability and stats
Determine whether the statements are true or false. A. In logistic regression, the model is fitted by using The Least Square Regression Estimation method. B. Odds ratio is defined as the ratio of two log-odds. C. In logistic regression, as Bo + Bx gets huge, p approaches 1.
2 The operator of a pumping station has observed that demand for water during early afternoon hours has an approximately exponential distribution with mean 100 cfs (cubic feet per second). (a) Find the probability that the demand will exceed 250 cfs during the early afternoon on a randomly selected day. (Round your answer to four decimal places.) (b) What water-pumping capacity, in cubic feet per second, should the station maintain during early afternoons so that the probability that demand will exceed capacity on a randomly selected day is only 0.02? (Round your answer to two decimal places.) cfs
Hanny
The answer is in red.
For numbers 2-7: A remission is when leukemia cannot be detected in the body and there are no symptoms. A total of 27 random sample of patients from a certain hospital was obtained. The Leukemia Remission data set has a response variable of whether leukemia remission occurred (Y=1). The predictor variables are cellularity of the marrow clot section (CELL) and proportion of absolute marrow leukemia cell infiltrate (INFIL). Regression analysis was done and the model is given by: In(1²(Y-1)) = -2.88 +3.08CELL - 2.5INFIL Macbee wants to validate the model above. He observed 30 random sample of patients from the same hospital. He came up with a confusion matrix below. Predicted Probability Outcome 0.5 0 (with parasite) 5 2 1 (without 1 20 parasite)