A petrol pump station has 4 pumps. The service times follow the exponential distribution with a mean of 6 minutes and cars arrive for service in a Poisson process at the rate of 30 cars per hour. (i) What is the probability that an arrival would have to wait in line?(ii) Find the average waiting time, the average time a car spent in the system and the average number of cars in the system. (iii) For what percentage of time would a pump be idle an an average?

Q: The average number of deaths from lung cancer in a certain population per year has been observed to…

A: Obtain the probability that during the current year fifteen or more people will die from lung cancer…

Q: The number of raisins in a randomly chosen Jamaican spice bun can be modeled as a random variable…

A: The random variable number of raisins follows Poisson distribution with mean 5.2.

Q: The number of earthquakes that occur per week 1.5. follows a Poisson distribution with a mean of (a)…

A: Introduction: It is required to obtain the Poisson probabilities using manual calculation, and R…

Q: The number of typing errors on a page follows a Poisson distribution with an average of 0.8 per…

A: The number of typing errors on a page follows a Poisson distribution with an average of 0.8 per…

Q: The number of purchases of artworks at a fine art gallery on a weekend day has a Poisson…

A:

Q: Manchester United is playing Liverpool at home in an English Premier League game this weekend. The…

A:

Q: 1. For the last 10 years, a certain school in Visayas has a passing rate of 63.25% for the bar exam.…

A: We have given that p = 63.25% = 0.6325 n = 245

Q: A travel centre has three service counters to receive people who visit to book air tickets. The…

A: The arrival rate is λ=100 persons10 hour=10 per hour Service time is μ=15 min per customer=4…

Q: The birth rate in a hospital is given to match the Poisson distribution with an average of 1.2 per…

A: Let us consider,  the number of births in a hospital is denoted by X. Then it is given that…

Q: he birth rate in a hospital is given to match the Poisson distribution with an average of 1.2 per…

A: Given Data: Let X represent the birth rate per hour   λ=1.2 X~ Poi (1.2)

Q: Use the Poisson distribution tables, not the mathematical formula.  It is estimated that 2% of the…

A: Given : 2% of the people in an auditorium of 100 unmarried/not related adults own a second home i.e…

Q: The number of typhoon occurring in the Philippines in a particular month is known to conform to the…

A: Given  Standard deviation of Poisson distribution=2 Variance of Poisson distribution=22=4 Mean and…

Q: What is the mean and standard deviation of the number of pedestrians waiting to cross? What is the…

A:

Q: (i) only one breakdown, (ii) at least one breakdown.

A:

Q: The arrival of airplanes at a one-runway airport follows a Poisson distribution with a mean rate of…

A: The arrival rate (λ) is 8 per hour.

Q: In a specific area, this period of time, it is believed that the number of thunderbolts that are…

A:

Q: Suppose that the number of accidents occuring in an industrial plant is described by a Poisson…

A:

Q: ABC bank has a single drive-in teller serving the customers in their cars. On average 13 customers…

A: Given:λ=1360=0.2167 per minuteμ=14=0.25 per minute

Q: If electricity power failures occur according to a Poisson distribution with an average of 3…

A:

Q: It is assumed that the number of patients who apply to a district hospital at night fits the Poisson…

A: Given: X~P(λ=4)

Q: The number of content changes to a Web site follows a Poisson distribution with a mean of 1 content…

A:

Q: The mean number of typhoon hitting US follows a Poisson distribution with     variance 0.5 per…

A: In general, the mean and variance of the Poisson distribution is same. Here, ?=0.5 per month. a)…

Q: The number of crashes of a mainframe computer in a college follows a Poisson distribution with an…

A: The Poisson distribution is given by, px; λ=e-λλxx! Here, x is the number of crashes of a mainframe…

Q: The number of people arriving for treatment at an emergency room can be modeled by a Poisson process…

A: Let X be the random variable from Poisson distribution with a rate parameter λ = 5 Then,  We will…

Q: Data from the Central Hudson Laboratory determined that the mean number of insect fragments in…

A: Given Information: In a 27-gram bar the mean number of insect fragments would then be 1.73. Assume…

Q: You work at a mechanic shop.  On average, 10 cars come into your shop each day.  Assuming a poisson…

A:

Q: The lifetime (years) of a television power adapter can be considered to follow a Weibull…

A: We have given that parameter for weibull distribution a = 15.0 and  b = 1.59

Q: For the case of the thin copper wire, suppose that the number of flaws follows a Poisson…

A: The probability mass function of the Poisson distribution is given by

Q: Complaints about an Internet brokerage firm occur at a rate of 1.4 per day. The number of complaints…

A: Let the random variable X be defined as the number of complaints received by the firm in a 3-day…

Q: The arrival rate of cars at PC jewelers is 20 cars per hour. The service rate at PC jeweler shop is…

A: At PC jewelers shop,The arrival rate of cars per hourThe service rate of cars per hourThe…

Q: Jamuna future park has one parking counter. From previous experience, it is estimated that cars…

A: “Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: A crew of mechanics at the Department of Transportation garage make minor repairs to snowplows…

A: Solution -The snowplows break down at an average rate=4 vehicles per day -an average the mechanic…

Q: The number of meteors found by a radar system in any 30-second interval under specified conditions…

A: The number of meteors found in any 30-second interval = 1.81 30 seconds =  0.5 minutes So, the…

Q: The number of traffic accidents at a certain intersection is thought to be well modeled by a Poisson…

A: Given that, the number of traffic accidents at a certain intersection is thought to be well modeled…

Q: The number of calls received by an office follows Poisson distribution with a mean of 8 calls.…

A: Answer: From the given data, Let X: number of calls received by an office follows X follows Poisson…

Q: The number of earthquakes per day in the world has a Poisson distribution with parameter ?= 55.…

A: Note:Hi there! Thank you for posting the question. As there are multiple sub parts, according to our…

Q: The mean number of customers arriving at a service station during the 25-minute period is 5. Find…

A: Let us denote X=the number of customers who will arrive at the service station during a 25-minute…