3. The time between arrivals of taxis at a busy intersection is exponentially distributed with a meanof 10 minutes.(a) What is the probability that you wait longer than one hour for a taxi?(b) Suppose you have already been waiting for one hour for a taxi, what is the probabilitythat one arrives within the next 10 minutes?(c) Determine x such that the probability that you wait more than x minutes is 0.10.(d) Determine x such that the probability that you wait less than x minutes is 0.90.(e) Determine x such that the probability that you wait less than x minutes is 0.50.

Answered: Image /qna-images/answer/210ba25a-141f-465d-a21f-3aede35d7673.jpg

Answered: 3. The time between arrivals of taxis…

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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The time (in minutes) between telephone calls at an insurance claims office has the exponential probability distribution: f(x)=0.50e-0.50x for x ≥ 0 What is the mean time between telephone calls? What is the probability of 30 seconds or less between telephone calls? What is the probability of 1 minute or less between telephone calls? What is the probability of 5 or more minutes without a telephone call?
express the event "taking atleast 16 credits" in terms of X and find its probability
Let's assume data collected at the Diamond Head State Monument sug- gests that an exponential distribution with mean value 2 hours is a good model for rainfall duration. What is the probability that the duration of a particular rainfall event at this location is at least 2 hours? At most 3 hours? Between 2 and 3 hours?
b. The lifetime X of a particular species is assumed to be exponentially distributed with mean 75 time units. Find the probability that a member of this particular species picked at random survives: i. more than 90 time units; less than 70 time units; between 70 and 85 time units. ii. iii. iv. Calculate Var(X).
The waiting time T at a bank teller’s window between two successive customers isdistributed as exponential with a mean of four minutes. Find the following probabilities:(a) P(T ≥ 5, (b) P(3 ≤ T ≤ 6), (c) P(T ≤ 4), and (d) P(T < 5). NOTE: Please explain each part, so the problem can be used as a Study Guide
Suppose the you have to take a bus to work. The amount of time until the next bus arrives follows an Exponential distribution with mean 7 minutes. (a) What is the probability that the next bus will arrive within 5 minutes? (b) 90% of all buses arrive within how many minutes of the previous bus? (c) Suppose the bus still has not arrived within 9 minutes of the last bus. Knowing that, what is the probability that the next bus will take at least 15 minutes to arrive? (d) Suppose that the amount of time the next bus arrives is independent of each next bus with the same distribution (Exponential with mean 7). What is the probability that the next bus arrives in less time than the next next bus (i.e. a second bus)?
The useful life of Johnson rods for use in a particular vehicle follows an exponential distribution with an average useful life of 5.2 years.You have a three-year warranty on your vehicle’s Johnson rod. What is the probability that the Johnson rod doesn’t fail before then? That is, what is the probability that its useful life doesn’t end before three years?b.If the vehicle manufacturer wants to limit the number of claims on the three-year warranty to 20%, what should the average useful life of the Johnson rod be?
Today, the waves are crashing onto the beach every 5.1 seconds. The times from when a person arrives at the shoreline until a crashing wave is observed follows a Uniform distribution from 0 to 5.1 seconds. Round to 4 decimal places where possible. The probability that a person will be born between weeks 18 and 52 is P(18<x<52)P(18<x<52) = The probability that a person will be born after week 40 is P(x > 40) = P(x > 10 | x < 47) =
A recent survey of 1040 U.S. adults selected at random showed that 634 consider the occupation of firefighter to have very great prestige. Estimate the probability (to the nearest hundredth) that a U.S. adult selected at random thinks the occupation of firefighter has very great prestige.Step 1Recall that the probability of an event based on relative frequency uses the formulaprobability of event = relative frequency = fn,where f is the frequency of the event occurrence in a sample of n observations. A total of 1040 people were surveyed and 634 considered the occupation of firefighter to have very great prestige. Therefore, the sample size is n = . The event of interest is that a U.S. adult selected at random thinks the occupation of firefighter has very great prestige. Therefore, the frequency f is equal to the number of adults who the occupation of firefighter has very great prestige, so f = (0.6096 answer is incorrect.) .
The time between failures of our video streaming service follows an exponential distribution with a mean of 40 days. Our servers have been running for 17 days, What is the probability that they will run for at least 97 days? (clarification: run for at least another 80 days given that they have been running 17 days). Report your answer to 3 decimal places.
Benford's Law claims that numbers chosen from very large data files tend to have "1" as the first nonzero digit disproportionately often. In fact, research has shown that if you randomly draw a number from a very large data file, the probability of getting a number with "1" as the leading digit is about 0.301. Suppose you are an auditor for a very large corporation. The revenue report involves millions of numbers in a large computer file. Let us say you took a random sample of n = 250 numerical entries from the file and r = 60 of the entries had a first nonzero digit of 1. Let p represent the population proportion of all numbers in the corporate file that have a first nonzero digit of 1. Test the claim that p is less than 0.301 by using α = 0.01. What does the area of the sampling distribution corresponding to your P-value look like? a. The area in the right tail of the standard normal curve. b. The area not including the right tail of the standard normal curve.…

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