Suppose that the useful life of a particular car battery, measured in months, decays with parameter...

Suppose that the useful life of a particular car battery, measured in months, decays with parameter 0.025. We are interested in the life of the battery. a. Define the random variable.

X = _________________________________.

b. Is X continuous or discrete?

c. X ~ ________

d. On average, how long would you expect one car battery to last?

e. On average, how long would you expect nine car batteries to last, if they are used one after another?

f. Find the probability that a car battery lasts more than 36 months.

g. Seventy percent of the batteries last at least how long?

Solutions

Expert Solution

orchestra answered 2 years ago

Next > < Previous

Related Solutions

Suppose the life of a particular brand of calculator battery is approximately normally distributed with a...

Suppose the life of a particular brand of calculator battery is approximately normally distributed with a mean of 75 hours and a standard deviation of 9 hours. a. What is the probability that a single battery randomly selected from the population will have a life between 70 and 80 hours? P(70 ≤ x ≤80)equals=0.4215 (Round to four decimal places as needed.) b. What is the probability that 4 randomly sampled batteries from the population will have a sample mean life...

Suppose the life of a particular brand of calculator battery is approximately normally distributed with a...

Suppose the life of a particular brand of calculator battery is approximately normally distributed with a mean of 80 hours and a standard deviation of 9 hours. Complete parts a through c. a. What is the probability that a single battery randomly selected from the population will have a life between 7575 and 85 hours? b. What is the probability that 99 randomly sampled batteries from the population will have a sample mean life of between 75 and 85 hours?...

Suppose the life of a particular brand of calculator battery is approximately normally distributed with a...

Suppose the life of a particular brand of calculator battery is approximately normally distributed with a mean of 75 hours and a standard deviation of 9 hours. What is the probability that 9 randomly sampled batteries from the population will have a sample mean life of between 70 and 80 hours?

One of the important features of a camera is the battery life as measured by the...

One of the important features of a camera is the battery life as measured by the number of shots taken until the battery needs to be recharged. The data shown in the table below contain the battery life of 10 subcompact and 10 compact cameras. Complete parts (a) through (c). Subcompact 49 50 25 28 31 33 39 57 47 57 Compact 70 30 60 35 55 39 59 46 52 68 . Assuming that the population variances from both...

A race car company developed a new car battery that has a longer life span than that...

A race car company developed a new car battery that has a longer life span than that of a traditional battery. From the date of purchase of a race car, the distribution of the life span of the new battery is approximately normal with mean 30 months and standard deviation 8 months. For the price of $50, the company offers a two-year warranty on the new battery for customers who purchase a race car. The warranty guarantees that the car will...

The average life of a particular model of shoes is 15 months. Someone in the research...

The average life of a particular model of shoes is 15 months. Someone in the research and development division of the shoe company claims to have developed a longer lasting product. This new product was worn by 30 individuals and lasted on average for 17 months. The variability of the original shoe is estimated based on the standard deviation of the new group which is 5.5 months. Is the designer's claim of a better shoe supported by the trial results?...

Let ? denote the life length, in hours, of a battery. Suppose ? is known to...

Let ? denote the life length, in hours, of a battery. Suppose ? is known to be normally distributed with standard deviation ? = 2.2 hours. A random sample of 16 batteries has an average life of ?̅ = 41.1 hours. We are interested in determining whether there is evidence to support the claim that mean battery life exceeds 40 hours. Using a level of significance of 0.05, answer the following questions. a.) State the null and alternative hypothesis for...

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...

Suppose the lifespan of a particular bran of calculator battery, X, is approximately normally distributed with...

Suppose the lifespan of a particular bran of calculator battery, X, is approximately normally distributed with a mean of 75 hours and a standard deviation of 10 hours. Please answer A-C (a) Let x̄ be the mean lifespan of a sample of n batteries. Does x̄ follow a normal distribution? Explain (b) What is the probability that a single randomly selected battery from the population will have a lifespan between 70 and 80 hours? (c) What is the probability that...

Suppose that the service life, in yours, of the "LOUD WHISPER", a hearing aid battery, is...

Suppose that the service life, in yours, of the "LOUD WHISPER", a hearing aid battery, is a random variable having a Weibull distribution with the Scale parameter = 0.7 and the Shape parameter = 2.1. a) What is the hazard rate at the second year of operation? b) What is the probability that the battery will fail between the first and third year? c) At what point in time, 30% of the batteries have died?

Subjects