14. The number of cars washed in a certain car wash station is a Poisson random variable witha mean of 6 cars per hour.(a) What is the probability that next car arriving to this station will wait less than 45minutes?(b) What is the probability that at least 1 cars will be washed in 30 minutes period?

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Answered: 14. The number of cars washed in a…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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A shop sells an average of 3 pieces of mobile telephones every day, what’s the probability that they’ll sell 4 phones today? (Poisson distribution)
33. In a manufacturing process where glass products are made, defects or bubbles occur, occasionally rendering the piece undesirable for marketing. It is known that, on average, 1 in 1000 of these items produced has one or more bubbles. What is the probability that a random sample of8000 will yield fewer than 7 items possessing bubbles using Poisson's Distribution?
Suppose that telephone calls arriving at a particular switchboard follow a Poisson process with an average of 4 calls coming per minute. What is the probability that up to a minute will elapse by the time 2 calls have come to the switchboard using the Gamma distribution? What is the probability that less than 30 seconds will elapse between successive calls coming to the switchboard? What is the probability of having at least 3 calls arrive to the switchboard in one minute? What is the probability of having at most 9 calls arrive to the switchboard in three minutes?
Suppose the number of cars in a household has a binomial distributionwith parameters n = 8, and p = 20 %.Find the probability of a household having:(a) 1 or 5 cars (b) 3 or fewer cars (c) 1 or more cars (d) fewer than 5 cars (e) more than 3 cars
5. Explain the following with respect to Random process, (i) Correlation ergodic processes
5. During the month of May, the number of calls received by the ITS Service Desk at Carleton University follows a Poisson distribution with a mean of 5 calls per hour. To answer each of the following questions, first define an appropriate random variable and identify its probability distribution and relevant parameter values. (a) What is the probability that more than two calls are received in a one-hour period? (b) What is the probability that exactly ten calls are received during a two-hour period? (c) If the ITS staff take a 30-minute break for lunch, what is the probability that they do not miss any calls? (d) Refer to part (c). What is the probability that the ITS staff do not miss any calls during lunch on at least three out five days?
Question 23 1 pts Given the sets: U {а, b, с, d, e, ...х, у, z} А — {d, e, h, і, о, р} C = {a, b, c, f, g, j, k, l, n, o , p, r, s, v, w, x} Find AUC' {a, b, c, d, e, f, g, h, i, j, k, I , m, n, o, p, q, r, s, t, u, v, w, x, y, z} {h, e, I, p} {a, e, i, o, u, y} {d, e, h, i, m, o, p, q, t, u, y, z}
One hundred people were surveyed, and one question pertained to their educational background. The results of this question and their genders are given in the following table. College degree (D) No college degree (D') Total 15 34 17 33 16 35 Female (F) Male (F') Total 33 50 35 50 68 100 17 15 32 Assuming these two events are independent, what is the expected value for the number of Females with a College degree?
The number of telephone calls that arrive at a call center is often modeled as a Poisson random variable. Assume that on average there are 10 calls per hour. What is the probability that there are less than 15 calls in two hours? (a)0.1847(b)0.2541(c)0.1049(d)0.3024
A survey of Salinas residents was conducted and the results on length of time in the workforce is presented below. 10 years Male 41 13 7 Female 39 21 10 When making a random selection from the table, what is the probability the individual has worked for less than 5 years or is a woman? [ Select ] When making two random selections from the table without replacement, find the probability both individuals are male. [ Select ]
5. The main Harvard exit gate has an outflow rate of 20 cars per minute which can be modeled as a Poisson Random Process. Suppose the east gate is also opened and given that cars choose it 30% of the time. What will be the new average time (in seconds) it takes for a car to exit the main gate? (Use 4 significant figures)

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