Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 5: Q. 5.13 (page 218)

At a certain bank, the amount of time that a customer spends being served by a teller is an exponential random variable with mean 5minutes. If there is a customer in service when you enter the bank, what is the probability that he or she will still be with the teller after an additional 4minutes?

Short Answer

Expert verified

The necessary probability of bank is around 0.45.

Step by step solution

01

Step :1   Random variables 

Establish Xas a variable quantity that represents the number of your time spent at the bank teller. We're given the knowledge that X~Expo⁡(λ)and EX=5, implying that λ=15. Assume there's a customer at the teller once we enter the bank. We are able to leverage the memoryless property of the exponential distribution, which states that we can reset time and observe from the beginning at any time. Assume there's a customer has only recently begun functioning at the teller. The likelihood that he will remain unmoved

02

Step :2 Substitution 

P(X>4)=1−P(X≤4)=1−1−e−15×4=e−45=0.45P(X>4)≈0.45

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

(a) A fire station is to be located along a road of length A,A<∞. If fires occur at points uniformly chosen on localid="1646880402145" 0,A, where should the station be located so as to minimize the expected distance from the fire? That is,

choose a so as to minimize localid="1646880570154" EX-awhen X is uniformly distributed over 0,A.

(b) Now suppose that the road is of infinite length— stretching from point 0outward to ∞. If the distance of a fire from point 0is exponentially distributed with rate λ, where should the fire station now be located? That is, we want to minimize EX-a, where X is now exponential with rate λ.

The annual rainfall (in inches) in a certain region is normally distributed with μ=40andσ=4. What is the probability that starting with this year, it will take more than 10years before a year occurs having a rainfall of more than 50 inches? What assumptions are you making?

A bus travels between the two cities A and B, which are 100miles apart. If the bus has a breakdown, the distance from the breakdown to city A has a uniform distribution over (0,100). There is a bus service station in city A, in B, and in the center of the route between A and B. It is suggested that it would be more efficient to have the three stations located 25,50,and75miles, respectively, from A. Do you agree? Why?

A model for the movement of a stock supposes that if the present price of the stock is s, then after one period, it will be either us with probability p or ds with probability 1−p. Assuming that successive movements are independent, approximate the probability that the stock’s price will be up at least 30 percent after the next 1000 periods ifu=1.012,d=0.990,andp=.52.

Every day Jo practices her tennis serve by continually serving until she has had a total of 50successful serves. If each of her serves is, independently of previous ones,

successful with probability .4, approximately what is the probability that she will need more than 100serves to accomplish her goal?

Hint: Imagine even if Jo is successful that she continues to serve until she has served exactly 100 times. What must be true about her first 100 serves if she is to reach her goal?
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Decision Maths

Read Explanation

Discrete Mathematics

Read Explanation

Pure Maths

Read Explanation

Statistics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free