A salesperson’s monthly expenses (in thousands of dollars) are exponentially distributed, with an average of 4.25 (thousand dollars).(a) Give the probability density function for the expenses.(b) Find the probability that the expenses are more than $10,000.

The probability density function for the length of time of postal clerk spends with a customer (equation down below). calculate the likelihood that a clerk will spend 4-5 min with a randomly picked customer

The graph to the right is the uniform probability density function for a friend who is x minutes late (a) Find the probability that the friend is between 5 and 25 minutes late (b) it is 10 AM. There is a 30% probability the friend will arrive within how many minutes? (a) The probability that the friend is between 5 and 25 minutes late is (Type an integer or a decimal Round to three decimal places as needed.) (b) There is a 30% probability the friend will arrive within minutes (Type a whole number) Ang 100 10 20 30x Tem

The table below shows an incomplete probability density function for X , the number of imperfections per batch of jeans that just came off a production line. What should the missing probability be? Provide the final answer as a decimal. x   P(X = x)  0 0.88 1 0 2

The estimated life of an electronic component (measured in months) follows the probability density function below: .x.e x > 0 f(x) = {4 elsewhere 1. Find the probability that estimated life is greater than 5. 2. Find the mean of the estimated life

Directions: The amount of time required to serve a customer at a bank has an exponential density function with mean 4 minutes. 1. Find the probability that a customer is served in less than 3 minutes. Probability = 2. Find the probability that serving a customer will require more than 6 minutes. Probability =

A company uses wood chips in the manufacture of processed wood pieces of various sizes. Suppose the tons of wood chips T used per day has a probability density function f(T) = 0.25e-0.25T (a) Find the probability of using more than 4 tons of wood chips in a day. (Round your answer to three decimal places.) (b) Find the number of tons 7 (to the nearest ton) so that the probability of using more than 7 tons in a day is 0.07. tons

Do you dislike waiting in line? A supermarket chain has used computer simulation and information technology to reduce the average waiting time for customers at 2,300 stores. Using a new system, which allows the supermarket to better predict when shoppers will be checking out, the company was able to decrease average customer waiting time to just 28 seconds.   (a)Assume that supermarket waiting times are exponentially distributed. Show the probability density function of waiting time at the supermarket. f(x) =                                               x ≥ 0         elsewhere (b) What is the probability that a customer will have to wait between 30 and 45 seconds? (Round your answer to four decimal places.)   (c) What is the probability that a customer will have to wait more than 2 minutes? (Round your answer to four decimal places.)

The multinomial joint probability mass function becomes the binomial probability mass function when k = O 1 O 2 00