a. To determine Find the probability that the person will sell more than 2,000 cups of coffee in a week. Explanation Calculation: The number of sold coffee in a coffee shop follows a normal distribution with mean 320 cups and the standard deviation 20 cups. The number of sold doughnuts in a coffee shop follows a normal distribution with mean 150 doughnuts and the standard deviation 12 doughnuts. The day to day sales are independent, Sunday, the coffee shop is closed. The distribution of coffee sales is normally distributed . Let X i be the number of sold cup of coffee in i th day. i = 1 , 2..6 Hence, total number of sold coffee is ∑ i = 1 6 X i . Here, E ( X i ) = 320 . Rule of expectation and standard deviation: If X be a random variable a and c are two constants, then, E ( a X + c ) = a E ( X ) + c V ( a X + c ) = a 2 V ( X ) S D ( a X + c ) = a S D ( X ) Addition rule of expectation: It is known that the expected value of the sum is the sum of the expected values. That is, is X and Y be random variables, with expected value, E ( X ) , E ( Y ) . Hence, the total expected value is E ( X ± Y ) = E ( X ) ± E ( Y ) . Using the rules, the expectation of ∑ i = 1 6 X i is, E ( ∑ i = 1 6 X i ) = ∑ i = 1 6 E ( X i ) = 6 × 320 = 1 , 920 Hence, the expected sold coffee is 1,920 in a week. Addition rule of Variance: It is known that the variance of the sum of two independent variables is the sum of their individual variances. That is, is X and Y be two independent random variables, with variances, V ( X ) , V ( Y ) . Hence, the total variance is V ( X ± Y ) = V ( X ) + V ( Y ) b. To determine Explain whether it is possible to expect in a day the shop’s profit is $300. c. To determine Find the probability that on any given day, he will sell a doughnut to more than half of his coffee customers.

21st Edition

ISBN: 9780137643219

Author: DeVeaux

Publisher: PEARSON

See similar textbooks

Concept explainers

Inverse Normal Distribution

The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of tw…

Mean, Median, Mode

It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency o…

Z-Scores

A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow compar…

Videos

Question

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

Chapter 14, Problem 53E

To determine

Find the probability that the person will sell more than 2,000 cups of coffee in a week.

To determine

Explain whether it is possible to expect in a day the shop’s profit is $300.

To determine

Find the probability that on any given day, he will sell a doughnut to more than half of his coffee customers.

Expert Solution & Answer

Learn your wayIncludes step-by-step video

See solution

Check out sample textbook solution

19:55

Chapter 14, Problem 52E

Chapter 14, Problem 54E

Chapter 14 Solutions

STATS:DATA+MODELS(LL)-W/ACCESS>CUSTOM<

Ch. 14.1 - 1. One of the authors took his minivan in for...Ch. 14.3 - 2. Suppose the time it takes a customer to get and...Ch. 14 - Prob. 1E Ch. 14 - 2. Caffeinated A coffee shop tracks sales and has...Ch. 14 - 3. Oranges again What is the standard deviation...Ch. 14 - 4. Caffeinated again What is the standard...Ch. 14 - 5. Salary An employer pays a mean salary for a...Ch. 14 - 6. Golf scores A golfer keeps track of his score...Ch. 14 - 13. Battery The life span of a calculator battery...Ch. 14 - 14. Ketchup An automatic filling machine in a...

Ch. 14 - 15. Expected value Find the expected value of each...Ch. 14 - 16. Expected value Find the expected value of each...Ch. 14 - 17. Pick a card, any card You draw a card from a...Ch. 14 - 18. You bet! You roll a fair die. If it comes up a...Ch. 14 - 19. Kids A couple plans to have children until...Ch. 14 - 20. Carnival A carnival game offers a $100 cash...Ch. 14 - 21. Software A small software company bids on two...Ch. 14 - Prob. 16E Ch. 14 - Prob. 17E Ch. 14 - Prob. 18E Ch. 14 - Prob. 19E Ch. 14 - 26. The die Find the standard deviation of the...Ch. 14 - Prob. 21E Ch. 14 - Prob. 22E Ch. 14 - Prob. 23E Ch. 14 - 30. Red lights A commuter must pass through five...Ch. 14 - 31. Defects A consumer organization inspecting new...Ch. 14 - 32. Insurance An insurance policy costs $100 and...Ch. 14 - Prob. 27E Ch. 14 - Day trading An option to buy a stock is priced at...Ch. 14 - Prob. 29E Ch. 14 - 36. Contracts Your company bids for two contracts....Ch. 14 - Prob. 31E Ch. 14 - Prob. 32E Ch. 14 - Prob. 33E Ch. 14 - Prob. 34E Ch. 14 - Random variables Given independent random...Ch. 14 - 42. Random variables Given independent random...Ch. 14 - Prob. 37E Ch. 14 - 44. Garden A company selling vegetable seeds in...Ch. 14 - Prob. 39E Ch. 14 - Stop! Find the mean and standard deviation of the...Ch. 14 - Tickets A delivery company’s trucks occasionally...Ch. 14 - Donations Organizers of a televised fundraiser...Ch. 14 - 49. Fire! An insurance company estimates that it...Ch. 14 - Prob. 45E Ch. 14 - 52. Pets The American Veterinary Association...Ch. 14 - Prob. 47E Ch. 14 - More pets You’re thinking about getting two dogs...Ch. 14 - 55. Medley In the 4 × 100 medley relay event, four...Ch. 14 - Prob. 50E Ch. 14 - Prob. 51E Ch. 14 - 58. Bike sale The bicycle shop in Exercise 56 will...Ch. 14 - 59. Coffee and doughnuts At a certain coffee shop,...Ch. 14 - Prob. 54E

Additional Math Textbook Solutions

Find more solutions based on key concepts

The F Distribution and the F-Ratio Use the following information to answer the next eight exercises. Groups of ...

Introductory Statistics

Standard Normal Distribution. In Exercises 13–16, find the indicated z score. The graph depicts the standard no...

Elementary Statistics (13th Edition)

In Exercises 25–28, use the confidence interval to find the margin of error and the sample mean. 25. (12.0, 14....

Elementary Statistics: Picturing the World (6th Edition)

1. The notation P(F|E) means the probability of event given event.

Fundamentals of Statistics (5th Edition)

Alvie Singer lives at 0 in the accompanying diagram and has four friends who live at A, B, C, and D. One day Al...

Probability and Statistics for Engineering and the Sciences

3. Hamsters How large are hamster litters? Among 47 golden hamster litters recorded, there were an average of 7...

Intro Stats

Knowledge Booster

$Statistics$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.

Recommended textbooks for you

MATLAB: An Introduction with Applications
Statistics
ISBN:9781119256830
Author:Amos Gilat
Publisher:John Wiley & Sons Inc
Probability and Statistics for Engineering and th...
Statistics
ISBN:9781305251809
Author:Jay L. Devore
Publisher:Cengage Learning
Statistics for The Behavioral Sciences (MindTap C...
Statistics
ISBN:9781305504912
Author:Frederick J Gravetter, Larry B. Wallnau
Publisher:Cengage Learning
Elementary Statistics: Picturing the World (7th E...
Statistics
ISBN:9780134683416
Author:Ron Larson, Betsy Farber
Publisher:PEARSON
The Basic Practice of Statistics
Statistics
ISBN:9781319042578
Author:David S. Moore, William I. Notz, Michael A. Fligner
Publisher:W. H. Freeman
Introduction to the Practice of Statistics
Statistics
ISBN:9781319013387
Author:David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:W. H. Freeman

MATLAB: An Introduction with Applications

Statistics

ISBN:9781119256830

Author:Amos Gilat

Publisher:John Wiley & Sons Inc

Probability and Statistics for Engineering and th...

Statistics

ISBN:9781305251809

Author:Jay L. Devore

Publisher:Cengage Learning

Statistics for The Behavioral Sciences (MindTap C...

Statistics

ISBN:9781305504912

Author:Frederick J Gravetter, Larry B. Wallnau

Publisher:Cengage Learning

Elementary Statistics: Picturing the World (7th E...

Statistics

ISBN:9780134683416

Author:Ron Larson, Betsy Farber

Publisher:PEARSON

The Basic Practice of Statistics

Statistics

ISBN:9781319042578

Author:David S. Moore, William I. Notz, Michael A. Fligner

Publisher:W. H. Freeman

Introduction to the Practice of Statistics

Statistics

ISBN:9781319013387

Author:David S. Moore, George P. McCabe, Bruce A. Craig

Publisher:W. H. Freeman

SEE MORE TEXTBOOKS

The Shape of Data: Distributions: Crash Course Statistics #7; Author: CrashCourse;https://www.youtube.com/watch?v=bPFNxD3Yg6U;License: Standard YouTube License, CC-BY

Shape, Center, and Spread - Module 20.2 (Part 1); Author: Mrmathblog;https://www.youtube.com/watch?v=COaid7O_Gag;License: Standard YouTube License, CC-BY

Shape, Center and Spread; Author: Emily Murdock;https://www.youtube.com/watch?v=_YyW0DSCzpM;License: Standard Youtube License