Suppose the lifetime of a certain model of car battery is assumed to follow an exponential...

Suppose the lifetime of a certain model of car battery is assumed
to follow an exponential distribution with a mean lifetime of 5
years.
a. What is the probability that the total lifetime of the
5 batteries will exceed 9.85 years?
b. How many car batteries would be needed to be 90% sure that
the total lifetime would exceed 25 years? c. For a sample of size n = 5, put into service at the same time
1) What is the probability the first failure occurs before
2 years?
2) What is the probability the time between the first and
second failure is less than 2 years?
3) What is the expected time of the last failure?

Expert Solution

orchestra answered 1 year ago

Lithium cellphone batteries for a certain model has a lifetime that follows an exponential distribution with...

Lithium cellphone batteries for a certain model has a lifetime that follows an exponential distribution with β = 3000 hours of continuous use. What is the probability that a randomly chosen battery would last at least 8 months? (assume 30 days in each month) 0.9920 c. 0.8253 e. 0.1466 0.9197 d. 0.8534 What is the probability that a randomly chosen battery lasts between 60 to 8 months? 0.0435 c. 0.0795 e. 0.1466 0.0903 d. 0.1457 What would be the lower...

The lifetime of a certain kind of battery is exponentially distributed, with an average lifetime of...

The lifetime of a certain kind of battery is exponentially distributed, with an average lifetime of 25 hours 4. Find the value of the 60th percentile for the lifetime of one battery. Remember units! 5. Write an interpretation (a sentence) of the 60th percentile for the lifetime of one battery. Your interpretation should include the value of the 60th percentile with correct units. 6. We are interested in the average lifetime of 16 of these batteries. Call this random variable....

A battery manufacturer claims that the lifetime (X) of a certain type of battery is normally...

A battery manufacturer claims that the lifetime (X) of a certain type of battery is normally distributed with a population mean of 40 hours and standard deviation 10 hours. (a) If the claim is true, what is P ( X ≤ 36.7 )? (b) Let X ¯ be the mean lifetime of the batteries in a random sample of size 100. If the claim is true, what is P ( X ¯ ≤ 36.7 )?

The lifetime of a certain type of batteries follows an exponential distribution with the mean of...

The lifetime of a certain type of batteries follows an exponential distribution with the mean of 12 hours. a) What is the probability that a battery will last more than 14 hours? (Answer: 0.3114) b) Once a battery is depleted, it is replaced with a new battery of the same type. Assumingindependence between lifetimes of batteries, what is the probability that exactly 2 batteries will be depleted within 20 hours? (Answer: 0.2623) c) What is the probability that it takes...

The usable lifetime of a particular electronic component is known to follow an exponential distribution with...

The usable lifetime of a particular electronic component is known to follow an exponential distribution with a mean of 6.1 years. Let X = the usable lifetime of a randomly selected component. (a) The proportion of these components that have a usable lifetime between 5.9 and 8.1 years is __. (b) The probability that a randomly selected component will have a usable life more than 7.5 years is __. (c) The variance of X is __.

The lifetime of a certain type of battery is normally distributed with a mean of 1000...

The lifetime of a certain type of battery is normally distributed with a mean of 1000 hours and a standard deviation of 100 hours. Find the probability that a randomly selected battery will last between 950 and 1000 (round answers to three decimal places, example 0.xxx)? The lifetime of a certain type of battery is normally distributed with a mean of 1000 hours and a standard deviation of 100 hours. Find the probability that a randomly selected battery will last...

5) The lifetime of a certain type of batteries follows an exponential distribution with the mean...

5) The lifetime of a certain type of batteries follows an exponential distribution with the mean of 12 hours. a) What is the probability that a battery will last more than 14 hours? b) Once a battery is depleted, it is replaced with a new battery of the same type. Assuming independence between lifetimes of batteries, what is the probability that exactly 2 batteries will be depleted within 20 hours? c) What is the probability that it takes less than...

1) The lifetime of 60W GE light bulbs are known to follow an exponential (skewed to...

1) The lifetime of 60W GE light bulbs are known to follow an exponential (skewed to the right) distribution. GE wants to test its own claim that the average lifetime of its 60W light bulbs is at least 1000 hours, so they test 10 bulbs at random (they don?t want to destroy too many) and calculate the mean and standard deviation of their sample. Which type of test should they perform? One-sample z-test since they know the true standard deviation...

5. The lifetime of a car battery can be modeled as a Weibull distribution with a=0.9....

5. The lifetime of a car battery can be modeled as a Weibull distribution with a=0.9. a) If the probability that a battery works longer than 10 years is 0.45, find the value of the parameter λ? b) What is the time to which 75% of the battery work?

The lifetime of a certain battery is normally distributed with a mean value of 20 hours...

The lifetime of a certain battery is normally distributed with a mean value of 20 hours and a standard deviation of 2.5 hours. a. What are the distribution parameters (μ and σ) of the sample mean if you sample a four pack of batteries from this population? b. If there are four batteries in a pack, what is the probability that the average lifetime of these four batteries lies between 18 and 20? c. What happens to the probability in...

Question