Question

The lifetime of a regular bulb is exponentially distributed with a mean of 25 days. What is the probability that you will need to replace the bulb in your room for five times in the year of 2020? (There are 365 days in 2020.)

Answer #1

The lifetime of a certain kind of battery is exponentially
distributed, with an average lifetime of 25 hours. 12. Draw a graph
to represent the probability that the average lifetime of 16
batteries is between 20 and 25 hours. Shade an appropriate region.
(See Question 8) Question #8 says: Find the probability that the
average lifetime of 16 batteries is between 20 and 25 hours.

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?

The lifetime of a calculator costing $250 is exponentially
distributed with mean 3 years. The manufacturer agrees to pay a
full refund to a buyer if the
calculator fails during the first year following its purchase,
and a one-half refund if it fails during the second year. If the
manufacturer sells 100
calculators how much should it expect to pay in refunds?

The time between failures for an appliances is exponentially
distributed with a mean of 25 months. What is the probability that
the next failure will not occur before 32 months have elapsed?
Report answer to 4 decimal places

The life of light bulbs is distributed normally. The variance of
the lifetime is 400 and the mean lifetime of a bulb is 530 hours.
Find the probability of a bulb lasting for at least 552 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 mean lifetime of a bulb is 570 hours.
Find the probability of a bulb lasting for at least 599 hours.
Round your answer to four decimal places.

The life of light bulbs is distributed normally. The variance of
the lifetime is 225 and the mean lifetime of a bulb is 520 hours.
Find the probability of a bulb lasting for at most 533 hours. Round
your answer to four decimal places.

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 light bulbs produced by a company are normally
distributed with mean 1500 hours and standard deviation of 125
hours.
a). What is the probability that a bulb will still be burning
after 1250 hours?
b). What is the number of hours that is survived by 78.81% of
the light bulbs?

Two turtles are racing. Turtle A’s time is exponentially
distributed with mean 2 minutes. Turtle B’s time is exponentially
distributed with mean 3 minutes. Assume that their times are
independent.
a) What is the probability that turtle A wins?
b) What is the expected time of the winner? What is its variance?
c) What is the pdf of the time difference between the loser and the
winner (by how much the faster turtle wins)?

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