Assume that arrivals follow a poisson probability distribution with 3 arrival rate per hour and the service times follow an exponential probability distribution with 6 service rate per hour. The probability that a new arrival has to wait for service 0.5 1. 0.3

Q: ve part is found. If 10 or more parts are tested unt ipment is accepted as meeting specifications.…

A: This is the case of geometric distribution.In this case, the probability of success will be…

Q: The time between arrivals of buses at a bus stand is exponentially distributed with a mean of 20…

A: Problem can be solved using exponential distribution formula.

Q: The number of industrial injuries per working week in a particular factory is known to follow a…

A: Given that  Mean =λ=0.5 X~poisson (λ) Where  λ ia a parameter.

Q: The number X of people entering the intensive care unit (ICU) in a particular Hospital on any one…

A: Number of people entering on any one day = 3, then Number of people entering on any two days = 2 × 3…

Q: The time between two telephone calls that arrive at a Police station is often modeled as an…

A: Exponential distribution is a continuous probability distribution. This indicates the time between 2…

Q: The waiting time at a railroad crossing follows an exponential distribution, with an average time of…

A:

Q: The time until the graduates of a department find their first jobs after graduation follows an…

A:

Q: The life of a power transmission tower is exponentially distributed, with mean life 25 years. If…

A:

Q: The time between arrival of buses follows an exponential distribution, with a mean of 20 minutes. •…

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

Q: A bakery produces an average of 50 loaves of bread per day. The number of loaves produced by the…

A: The objective of this question is to find the probability that the bakery will sell at least two…

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…

Q: Delivery times for shipments from a central warehouse are exponentially distributed with a mean of…

A: Central Limit Theorem for mean: If a random sample of size n is taken from a population having mean…

Q: Make a histogram of the probability distribution of X. Describe its shape.

A: The given random variable X is the number that survive to adulthood.

Q: Customers arrive at a counter at the rate of 8 per hour. Assume the arrivals have a Poisson…

A: 15 minutes= 1560=0.25 hoursGiven that customers arrive at a counter at the rate of 8 per hour.So, in…

Q: The life of a light bulb is exponentially distributed with a mean of 1,000 hours. What is the…

A: Given that mean= 1000  So, Let X= number of hours that the bulb will last So, X follows an…

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!