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.)

Q: Exainipie r A probability curve y = f(x) has a range 0 to o. If f(x) = e*, Find the mean, variance…

A: The mean value of a continuous random variable is computed by integrating the multiplication of…

Q: The lifetime, t, in hours, of an alkaline battery is exponentially distributed with ? = 0.10 per…

A: The lifetime in hours of an alkaline battery is exponentially distributed with λ=0.10 per hour. The…

Q: Consider a financial instrument which follows an Arithmetic Brownian Motion with zero drift and…

A: Given  Arithmetic Brownian Motion Drift 0 Volatility 1

Q: Many electronics follow a failure rate described by an exponential probability density function…

A:

Q: =) Find u and o.

A:

Q: The average fuel consumption of a house, in kg/day, can be modeled by a lognormal distribution where…

A: We have given that  The average fuel consumption of a house, in kg/day, can be modeled by a…

Q: What is the key advantage of the Logit Model over the Linear Probability Model?

A: Logic model- It is also defines as logistic Regression, is a binomial regression model. It  is used…

Q: Determine the distribution function for the Pareto(a) distribution of the logistic distribution of…

A: Let X be a random variable having having basic Pareto Distribution with shape parameter α. The PDF…

Q: Many electronics follow a failure rate described by an exponential probability density function…

A: Introduction: Denote X as the time to failure of the solar panel of the given make.

Q: When you are conducting the t test, the population does NOT need to be approximately normally…

A: one of the assumption for conducting t-test is that when you are conducting t-test the population…

Q: Statistics and Probability In a M/M/1 model, the average number of customers in the system is 6, and…

A: Given information is ; Number of customers in the system (Ls)=6 Average waiting time in the queue…

Q: please solve explain both part a and b for my understanding

A: The total number of balls is 8, with 4 black and 4 white. When two balls are drawn without…

Q: The following logit model of house ownership is estimated. Y, = -1, 4097 +0,0326.X, where Y=1 if the…

A: There seems to be a typo in the equation. We assume that comma was mistakenly typed instead of…

Q: A pressure transducer regulates a climate control system in a factory. Thetransducer fails according…

A: Distribution function Ft=1-e-λt Density function ft=λe-λt

Q: certain type of battery has an average lifetime of 60 hours. Assume that the battery’s lifespan is…

A: The  exponential probability density function is given by- fx=λe-λx,x≥0 The mean of function is-…

Q: Construction workers use sturdy overalls when working. An overall on average lasts for 6 months…

A:

Q: The probability that you will receive a wrong number call this week is 0.1. The probability that you…

A: From the provided information, Let A represent the event that he will receive a wrong number call…

Q: Over time, the number of original basicwords in a language tends to decrease as words becomeobsolete…

A: We know exponential distribution function is defined by  f(x)=e-ax for x in [0,∞). Here we have…

Q: I don't understand this.

A: The objective of the question is to find the probability distribution of T, where T is the number of…

Q: Investigators evaluated the effect of education (E1=1 if college or more, E2=1 if Masters degree or…

A: The logistic regression model is given by:To find:The odds of having a job for someone with a…

Q: Two pilots (X and Y) are assigned to a flight from Atlanta to Chicago. Both need to be in the…

A: Given the random variables X and Y be the delay for the flight from Cedar Rapids and delay for the…

Q: The percent of persons (ages five and older) in each state who speak a language at home other than…

A: From the provided information, The probability distribution function of exponential distribution…

Q: Suppose a fair die is thrown twice. Let us consider the following variable random: X = the maximum…

A: Introduction: Denote X1 as the outcome on the first throw, and X2 is the outcome on the second…

Q: On the basis of data collected from metal shredders across the nation, the amount x of extractable…

A: Given,A random variable X~Exponential(θ=12.5)f(x)=12.5e-x2.5         ;  x≥0

Q: Assume that there is a rare disease. It occurs in the population at a rate of 1 per 1000; that is,…

A: The probability that the patient have positive test when disease is present is 0.95. The probability…

Q: (ii) If it is known that the supercapacitor has been working 950 hours, what is the probability that…

A:

Q: Investigators evaluated the effect of education (E1=1 if college or more, E2=1 if Masters degree or…

A: The provided information is as follows:The effect of education is E1 is 1 if the individual has a…

Q: The amount of water flowing over a damn in any 30 minute interval follows a lognormal distribution…

A: Let X denote the amount of water flowing over a damn in any 30 minute interval follows a lognormal…

Q: The probability density function for the diameter of a drilled hole in millimeters is 10 e-10(x-5)…

A: Given: The probability density function for the diameter of a drilled hole in millimeter is given as…

Q: Reliability testing of the new 2.0 liter Chevy automotive engine has resulted in a time to failure…

A: Given information: tmed=90,000 miless=0.60

Q: robability that the plant will not be inundated for a period of 5 years? [Note the mean rate of…

A: Given: Probability of inundation  = 0.020 Mean rate if flood for inundation per year  = 0.012 Mean…

Q: John bought a second-hand car that was driven 16 kilometers (km) from sahibindenmiacaba.com. What is…

A:

Q: Read the question carefully and give me both a&b  right solution according to the question. A…

A: We have A catalyst powder has the following weight distribution in the given particle size range:…

Q: (b) The lifetime of a supercapacitor manufactured by ELEMENT45 is exponentially distributed with…

A: (b) (i) It is been asked to find the probability that super capacitor component is still working at…

Q: (4) Find the conditional probability that the watch has an operational lifetime in excess of 5 years…

A: Given:

Q: O The probability density function is f(x) = 2e-kx %3D i) Standard deviation of x = ?. %3D

A:

Q: When the Titanic sank in 1912, there were over 1,300 passengers aboard. A random sample of 50…

A:

Q: Suppose that X has a lognormal distribution with parameters 0 = 2 and w² = 9. Determine the…

A: Note:  P-value is taken from standard normal distribution table.

Q: A toy factory produces battery operated toy robots for toddlers. Previous research shows that the…

A: It is given that the lifetime of robots (say X) is exponentially distributed with a mean of 6…

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!