Answered: 3. The lifetime of a lightbulb in a…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

3. The lifetime of a lightbulb in a certain application is normally distributed with mean μ = 1400 hours
and standard deviation σ = 200 hours.
a. What is the probability that a lightbulb will last more than 1800 hours?
b. Find the 10th percentile of the lifetimes.
c. A particular lightbulb lasts 1645 hours. What percentile is its lifetime on?
d. What is the probability that the lifetime of a lightbulb is between 1350 and 1550 hours?

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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