Question

In: Statistics and Probability

The lifetime of a particular bulb is a random variable with an average of μ =...

The lifetime of a particular bulb is a random variable with an average of μ = 2000 hours and a standard deviation of σ = 200 hours.

(a) What is the probability that a bulb has a lifetime between 2000 and 2400 hours?

(b) What is the probability that a bulb will last less than 1470 hours?

(c) In the case that a bulb lasts for more than 2100 hours, the probability that it will last more than 2300 hours You calculate.

(d) the probability of a bulb lasting less than 2150 hours when it lasts for more than 2050 hours. You calculate.

Solutions

Expert Solution


Related Solutions

The lifetime of a particular bulb is a random variable with an average of μ =...
The lifetime of a particular bulb is a random variable with an average of μ = 2000 hours and a standard deviation of σ = 200 hours. (c) Calculate the probability that a bulb will last more than 2300 hours if it lasts longer than 2100 hours. (d) Calculate the probability that a bulb will last less than 2150 hours if it has lasted more than 2050 hours.
Lifetime of a particular laptop is exponential random variable with average of 5 years. A company...
Lifetime of a particular laptop is exponential random variable with average of 5 years. A company orders 100 of such laptops. Find the probability that there are more than 20 laptops still in operation after 6 years from the date of purchase. (Hint: First compute the probability of one laptop still being in operation after 6 years. That will be the probability of ”success”. Then compute the probability that you’ve at least 20 out of 100 with that property.)
For a particular machine, its useful lifetime (random variable T) is modeled by an exponential probability...
For a particular machine, its useful lifetime (random variable T) is modeled by an exponential probability density function. Given that the expected lifetime of this machine is 10 years, find the exponential probability density function f(t) for random variable T
For a particular machine, its useful lifetime (random variable T) is modeled by an exponential probability...
For a particular machine, its useful lifetime (random variable T) is modeled by an exponential probability density function. Given that the expected lifetime of this machine is 10 years, find the exponential probability density function f(t) for random variable T
The average lifetime of a light bulb is 3000 hours with a standard deviation of 696...
The average lifetime of a light bulb is 3000 hours with a standard deviation of 696 hours. A simple random sample of 36 bulbs is taken. What is the probability that the average life in the sample will be greater than 3219.24? Note: respond in decimal form, for example, if your solution is 87.1234%, you should enter in 0.871234.
The average lifetime of a light bulb is 2850 hours with a standard deviation of 400....
The average lifetime of a light bulb is 2850 hours with a standard deviation of 400. A simple random sample of 30 bulbs is taken. What is the probability that the average life in the sample will be between 2600 and 2700 hours?
Recall the lifetime (in months) of a battery is modeled by a random variable X that...
Recall the lifetime (in months) of a battery is modeled by a random variable X that has pdf fθ(x)=Kθx1(x>0)where K=ln(1/θ) for an unknown parameter θ∈(0,1) . Assume instead that we cannot actually observe the lifetime of the batteries. Instead, we only observe if the battery is still working after τ months for some known τ to be chosen later (this is called censored data ). Let Y1,…,Yn be our observations where Yi=1(Xi>τ) indicates that the i th battery is still...
For a random variable that is normally distributed, with μ = 80 and σ = 10,...
For a random variable that is normally distributed, with μ = 80 and σ = 10, determine the probability that a simple random sample of 25 items will have a mean between 78 and 85? a. 83.51% b. 15.87% c. 99.38% d. 84.13%
If X is a normal random variable with mean ( μ ) = 50 and standard...
If X is a normal random variable with mean ( μ ) = 50 and standard deviation ( σ ) = 40, then the probability of X > 80 is: a. 0.0000 b. 0.7734 c. 1.0000 d. 0.2266
If the weight of the students expressed by ?“a random variable” with a distribution of N(μ,...
If the weight of the students expressed by ?“a random variable” with a distribution of N(μ, σ), find: ?(? − ( ? 3 )? ≤ ? ≤ ? + ( ? 3 ) ?). 2. It assumed that the maximum temperature in Oman is normally distributed with a mean of D and a standard deviation of D/2 for which: ?(? − ? ≤ ? ≤ ? + ?) = 0.5934. calculate the value of “ ? “ Note: (D=8)
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT