Question

Let X denote the lifetime of a light bulb of a certain brand. Suppose that the lifetime of a light bulb of this particular brand has an exponential distribution with mean lifetime of 200 hours. What is the probability that a light bulb has a lifetime between 100 and 400 hours?

Answer #1

The probability that a light bulb has a lifetime between 100 and
400 hours is **0.4712.**

Suppose that for a particular brand of
light bulb, the lifetime (in months) of any randomly selected bulb
follows an exponential distribution, with parameter l = 0.12
a) What are the mean and standard deviation for
the average lifetime of the particular brand of light bulbs? What
is the probability a single bulb will last greater than 9
months?
b)
If we randomly select 25 light bulbs of the particular
brand, what are the mean and standard...

The lifetime of a certain brand of electric light bulb is known
to have a standard deviation of 53 hours. Suppose that a random
sample of 100 bulbs of this brand has a mean lifetime of 481 hours.
Find a 99% confidence interval for the true mean lifetime of all
light bulbs of this brand. Then complete the table below. Carry
your intermediate computations to at least three decimal places.
Round your answers to one decimal place. (If necessary, consult...

The lifetime of a certain brand of electric light bulb is known
to have a standard deviation of
51
hours. Suppose that a random sample of
150
bulbs of this brand has a mean lifetime of
481
hours. Find a
90%
confidence interval for the true mean lifetime of all light
bulbs of this brand. Then complete the table below.
Carry your intermediate computations to at least three decimal
places. Round your answers to one decimal place. (If necessary,
consult...

The lifetime of a light bulb in a certain application is
normally distributed with mean = 1000 hours and a
standard deviation = 100 hours.
A) What is the probability that a lightbulb will last more than
1100 hours?
B) Find the 10th percentile of the
lifetimes
C) What is the probability that the lifetime of a light
bulb is between 900 and 1100 hours?

Suppose that a certain brand of light bulb has a mean life of
450 hours and a standard deviation of 73 hours. Assuming the data
are bell-shaped: (Show work to get full credit)
a. Would it be unusual for a light bulb to have a life span of
320 hours? 615 hours? Justify each response.
b. According to the Empirical Rule, 99.7% of the light bulbs
have a lifetime between what two values?
c. Determine the percentage of light bulbs...

It is known that the lifetime of a certain type of light bulb is
normally distributed with
a mean lifetime of 1,060 hours and a standard deviation of 125
hours. What is the
probability that a randomly selected light bulb will last
between 1,000 and 1,100 hours?

Problem 7
Suppose you have a random variable X that represents the
lifetime of a certain brand of light bulbs. Assume that the
lifetime of light bulbs are approximately normally distributed with
mean 1400 and standard deviation 200 (in other words X ~ N(1400,
2002)).
Answer the following using the standard normal distribution
table:
Approximate the probability of a light bulb lasting less than
1250 hours.
Approximate the probability that a light bulb lasts between 1360
to 1460 hours.
Approximate...

Two light bulbs, have exponential lifetime where expected
lifetime for bulb A is 500 hours and expected lifetime for bulb B
is 200 hours.
a) What is the expected time until bulb A or bulb B malfunctions
?
b) What is the probability that bulb A malfunctions before bulb
B ?

It is assumed that the lifetime of a light bulb attached to the
entrance of a home follows a normal distribution N(180,100). When
it is replaced on New Year day, what is the probability that it
have to be replaced more than once (≧2) in the year?
(The answer should be rounded to the third decimal place and answer
to the second decimal place such as 0.12.)
Hint 1:
Let X be the lifetime of the first light bulb, and...

The life duration for a light bulb is well approximated by an
exponential random variable with a mean of 400 hours. Assume that a
classroom has a projector that has a life bulb with a lifetime
distribution as above, and it is used 40 hours per week. Also, for
your calculations, assume that a month has exactly 4 weeks.
What is the probability that you would need to replace the bulb
no more than twice a year? Assume uniform usage...

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