A type of lightbulb is labeled as having an average lifetime of 1000 hours.
(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 μ = 1000.
(i) Use this model to find the probability that a bulb fails within the first 500 hours (Round your answer to three decimal places.)
(ii) Use this model to find the probability that a bulb bums for more than 700 hours.
(b) What is the median lifetime of these lightbulbs? (Round your answer to one decimal place.)
Homework Answers
Add Answer to:
A type of lightbulb is labeled as having an average lifetime of 1000 hours.
(a) A lamp has two bulbs of a type with an average lifetime of 1300 hours.
(a) A lamp has two bulbs of a type with an average lifetime of 1300 hours. Assuming that we can model the probability of failure of these bulbs by an exponential density function with mean u = 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...
2. Light bulbs are known to have an average lifetime of 2,000 hours. Suppose we model...
2. Light bulbs are known to have an average lifetime of 2,000 hours. Suppose we model the lifetime of a light bulb by the following probability density function with (yet unknown) parameter c: p(t) = 1-e-t/c when t20 and p(t) = 0 otherwise. (a) Determine the value of the parameter c so that the probability density function has mean 2,000 hours. (b) Determine the probability a lightbulb fails before 1,500 hours. (C) Suppose the lightbulb has already been on for...
The lifetime of a type-A bulb is exponentially distributed with parameter λ. The lifetime of a...
The lifetime of a type-A bulb is exponentially distributed with parameter λ. The lifetime of a type-B bulb is exponentially distributed with parameter μ, where μ>λ>0. You have a box full of lightbulbs of the same type, and you would like to know whether they are of type A or B. Assume an a priori probability of 1/4 that the box contains type-B lightbulbs. Assume that λ=3 and μ=4. Find the LMS estimate of T2, the lifetime of another lightbulb...
3. Let and be independent random variables representing the lifetime (in 100 hours) of Type A...
3. Let and be independent random variables representing the lifetime (in 100 hours) of Type A and Type B light bulbs, respectively. Both variables have exponential distributions, and the mean of X is 2 and the mean of Y is 3. a) Find the joint pdf f(x, y) of X and Y. b) Find the conditional pdf fa(ylx) of Y given Xx. c) Find the probability that a Type A bulb lasts at least 300 hours and a Type B...
Lightbulbs of a certain type are advertised as having an average lifetime of 750 hours. The...
Lightbulbs of a certain type are advertised as having an average lifetime of 750 hours. The price of these bulbs is very favorable, so a potential customer has decided to go ahead with a purchase arrangement unless it can be conclusively demonstrated that the true average lifetime is smaller than what is advertised. A random sample of 50 bulbs was selected, and the sample mean was found to be 738.44 with a standard deviation of 38.20 and a standard error...
Lightbulbs of a certain type are advertised as having an average lifetime of 750 hours. The...
Lightbulbs of a certain type are advertised as having an average lifetime of 750 hours. The price of these bulbs is very favorable, so a potential customer has decided to go ahead with a purchase arrangement unless it can be conclusively demonstrated that the true average lifetime is smaller than what is advertised. A random sample of 50 bulbs was selected, and the sample mean was found to be 738.44 with a standard deviation of 38.20 and a standard error...
The lifetime of traditional light bulbs measured in hours is known to be normally distributed with...
The lifetime of traditional light bulbs measured in hours is known to be normally distributed with μ=100 and σ=20. What is the probability that a randomly selected traditional light bulb will have a lifetime of 125 hours or longer? You need to use a normal distribution table. Find the nearest answer. a. 4.006% b. 22.663% c. 10.565% d. 77.337% e. 89.435%
The life of light bulbs is distributed normally. The variance of the lifetime is 400400 and...
The life of light bulbs is distributed normally. The variance of the lifetime is 400400 and the mean lifetime of a bulb is 600600 hours. Find the probability of a bulb lasting for at most 633633 hours. Round your answer to four decimal places.
The life of light bulbs is distributed normally. The variance of the lifetime is 625 and...
The life of light bulbs is distributed normally. The variance of the lifetime is 625 and the mean lifetime of a bulb is 510 hours. Find the probability of a bulb lasting for at most 527 hours. Round your answer to four decimal places.
The life of light bulbs is distributed normally. The variance of the lifetime is 625 and...
The life of light bulbs is distributed normally. The variance of the lifetime is 625 and the mean lifetime of a bulb is 570 hours. Find the probability of a bulb lasting for between 532 and 599 hours. Round your answer to four decimal places.
2. Light bulbs are known to have an average lifetime of 2,000 hours. Suppose we model the lifetime of a light bulb by the following probability density function with (yet unknown) parameter c: p(t) = 1-e-t/c when t20 and p(t) = 0 otherwise. (a) Determine the value of the parameter c so that the probability density function has mean 2,000 hours. (b) Determine the probability a lightbulb fails before 1,500 hours. (C) Suppose the lightbulb has already been on for...
3. Let and be independent random variables representing the lifetime (in 100 hours) of Type A and Type B light bulbs, respectively. Both variables have exponential distributions, and the mean of X is 2 and the mean of Y is 3. a) Find the joint pdf f(x, y) of X and Y. b) Find the conditional pdf fa(ylx) of Y given Xx. c) Find the probability that a Type A bulb lasts at least 300 hours and a Type B...
The life of light bulbs is distributed normally. The variance of the lifetime is 625 and the mean lifetime of a bulb is 570 hours. Find the probability of a bulb lasting for between 532 and 599 hours. Round your answer to four decimal places.
Most questions answered within 3 hours.
-
You capture data by having 8 people fill in 30 small dots on a
piece of...
asked 1 hour ago -
What are the z-values such that 70% of the area lies in the
middle of the...
asked 2 hours ago -
You borrow $29,500 to purchase a brand new car. The interest
rate is 6%, and the...
asked 2 hours ago -
The amount of time it takes an asteroid, whose average distance
from the Sun is 4.70...
asked 2 hours ago -
A 0.289 kg mass slides on a frictionless floor with a speed of
1.34 m/s. The...
asked 2 hours ago -
15.A box contains five red balls, three green balls, and two
yellow balls. Suppose you select...
asked 5 hours ago -
Assume you are given the following for Stackelberg industries:
Return on Assets (ROA) = 8%
Debt...
asked 4 hours ago -
an engineer proposes to use mmWave in 5G network to
increase data rate.
What are the...
asked 4 hours ago -
Explain the idea behind using SEMIJOIN in distributed
query processing.
asked 4 hours ago -
why
is context important in selecting and applying guidelines and
principles for interface design?
illustrate your...
asked 4 hours ago -
In a certain board game, a player rolls two fair six-sided dice
until the player rolls...
asked 5 hours ago -
You are going to deposit $3,200 in an account that pays .58
percent interest compounded quarterly....
asked 4 hours ago