The number of kilometers that a car can run before the battery needs to be replaced is an exponential random variable with mean 20,000 km. I have not yet changed the battery in my car and I have driven it 15,000 kilometers. I am about to take a trip of 5,000 kilometers. What is the probability that I will be able to complete the trip without having to change the battery? O 0.3333 0.779 0.368 0.221 0.632

A random sample of n = 65 observations is selected from a population with a mean of 25 and s = 16. What is the probability that the sample mean is less than 16?

A believer in the "random walk" theory of stock markets thinks the value of an index of stock prices has a 0.6 probability of rising in any year. The change in the value of the index in any given year is not affected by whether it rose or fell in earlier years. You plan to record the value for the index in each of the next eight years. Let the random variable, X, represent the number of years (out of the next 8 years) in which the value of the index rises. a) If X is distributed according to the binomial probability distribution, what are the values for n and p?o b) What are the possible values X can take, or equal? QMETH 201, Homework 3 c) Calculate the probability X = 30 d) Calculate the expected value for X. e) Calculate the standard deviation for X. 4

A machine can process two online applications in 60 minutes. Answer the following questions. What would be an appropriate random variable? What would be the exponential-distribution counterpart to the random variable? Identify the mean of x, where x = minutes until the next occurrence and determine the following:  P (x ≥ 30.0) P (x ≤ 10) The machine must be disconnected for service for 45 minutes. What is the probability that an online application will be sent while the machine is out of service?

Autism Psychiatrists estimate that about 1 in 100 adultshas autism. What’s the probability that in a city of 20,000,there are more than 300 people with this condition? Besure to verify that a Normal model can be used here.

Say you’re a chemical engineer studying whether a certain trace impurity is present in aproduct. An experiment has a probability of 0.80 of detecting the impurity if it is present. Theprobability of not detecting the impurity if it is absent is 0.90. You have reason to believe that40% of products actually contain the impurity. You perform an experiment which detected animpurity – what is the probability that the impurity is not really there?

The lifetime of a lightbulb can be modeled with an exponential random variable with an expected lifetime of 1000 days. a. Find the probability that the lightbulb will function for more than 2000 days. b. Find the probability that the lightbulb will function for more than 2000 days, given that it is still functional after 500 days.

Note : Please solve within 30 minutes with a clear explanation. Suppose that a light fixture has 100 light bulbs installed. The lifetimes of light bulbs are independent exponential random variables with a common mean equal to 800 hours. Because replacing a light bulb involves someone climbing up the fixture, the owner decides not to replace bulbs until 5 light bulbs have burned out. If currently all the 100 light bulbs are working, find the expected time until the needs to replace the bulbs.

A sample of 400 adults found that 82  have high blood pressure. However, 98 of those studied reported being unwilling to change their diet. Based on this sample, if an adult is chosen at random, what is the probability that he or she is open to trying to eat more healthfully? Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.

If you select a random sample of 15 items from a large batch in which there are 18% defective items, what is the chance you find more than one defective items in the sample? Round your answer to 4 decimal places. Suppose the probability of a person having the disease is 0.20, and a sample of 23 individuals is tested. What is the probability that no individual in this sample will have a disease? Round your answer to 4 decimal places. Suppose the probability of a person having the disease is 0.20, and a sample of 23 individuals is tested. What is the expected number of people with the disease in this sample. Do not round your answer.