Question

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 deviation of the sampling distribution of average lifetimes of samples of 25 bulbs? What is the probability the sample of bulbs will last greater than 9 months on average?

Answer #1

a)

Lets' say l = λ = 0.12

**ß = mean = E[x] = 1/λ = 8.33
months**

variance = 1/λ² = 69.44444444

**std dev = √variance =
8.33**

Mean great than 9 probability will be:

**P ( X > 9 ) = e^(-x/ß) =
0.3396**

**b)**

Mean of sample in case of exponential distribution will be equal to that of population.(Central Limit theorem)

Mean = **8.33 months**

**Standard deviation = Standard deviation of
Population/sqrt(n) = 8.33/sqrt(25) = 8.33/5 = 1.666**

Now P(mean of sample > 9) = P(z> (mean - 9)/standard
deviation

=P(z> (8.33 - 9)/ 1.666 = P(z> (8.33 - 9)/ 1.666

=P(z> -0.40216)

**=0.6562**

**Please revert back in case of any doubt.**

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...

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...

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?

8.A manufacturing company of light bulb claims that an average
light bulb lasts 500 days. A contractor randomly selects 30 bulbs
for testing. The sampled bulbs last an average of 490 days, with a
standard deviation of 100 days. If the claim were true, what is the
probability that 30 randomly selected bulbs would have an average
life of no more than 490 days?

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 ?

Suppose that the lifetimes of light bulbs are approximately
normally distributed, with a mean of 57 hours and a standard
deviation of 3.5 hours. With this information, answer the
following questions.
(a) What proportion of light bulbs will last more than 61
hours?
(b) What proportion of light bulbs will last 51 hours or
less?
(c) What proportion of light bulbs will last between 58 and 61
hours?
(d) What is the probability that a randomly selected light bulb
lasts...

Suppose that the lifetimes of light bulbs are approximately
normally distributed, with a mean of 56 hours and a standard
deviation of 3.2 hours. With this information, answer the
following questions.
(a) What proportion of light bulbs will last more than 60
hours?
(b) What proportion of light bulbs will last 52 hours or
less?
(c) What proportion of light bulbs will last between 59 and 62
hours?
(d) What is the probability that a randomly selected light...

Suppose that the lifetimes of light bulbs are approximately
normally distributed, with a mean of 57 hours and a standard
deviation of 3.5 hours. With this information, answer the
following questions. (a) What proportion of light bulbs will last
more than 61 hours? (b) What proportion of light bulbs will last
51 hours or less? (c) What proportion of light bulbs will last
between 59 and 62 hours? (d) What is the probability that a
randomly selected light bulb lasts...

The lifetimes of a certain brand of LED light bulbs are normally
distributed with a mean of 53,400 hours and a standard deviation of
2500 hours.
A. If the company making these light bulbs claimed that they
would last at least 50,000 hours. What proportion of light bulbs
would meet the claim and last at least 50,000 hours? (12)
B. The company’s marketing director wants the claimed figure to
be where 98% of these new light bulbs to last longer...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 20 seconds ago

asked 1 minute ago

asked 6 minutes ago

asked 6 minutes ago

asked 9 minutes ago

asked 13 minutes ago

asked 13 minutes ago

asked 14 minutes ago

asked 20 minutes ago

asked 20 minutes ago

asked 34 minutes ago

asked 34 minutes ago