---**Title: Promotional Policy Analysis for a Supermarket****Introduction:**The management of a supermarket wants to adopt a new promotional policy of giving a free gift to every customer who spends more than a certain amount per visit at this supermarket. The expectation of the management is that after this promotional policy is advertised, the expenditures for all customers at this supermarket will be normally distributed with a mean of $95 and a standard deviation of $20. **Problem Statement:**If the management wants to give free gifts to at most 10% of the customers, what should the amount be above which a customer would receive a free gift?**Analysis:**Given that the expenditures are normally distributed with:- **Mean (µ)** = $95- **Standard deviation (σ)** = $20We need to find the expenditure amount (let's denote it as *X*) above which the top 10% of customers' expenditures lie. ### Solution:1. **Determine the Z-score** corresponding to the top 10%. The cumulative probability for the bottom 90% is 0.90. Using a Z-table or standard normal distribution calculator, the Z-score for 0.90 is approximately 1.28 (since 90% of the data lies below this point).2. **Apply the Z-score formula** to find X:\[ Z = \frac{X - \mu}{\sigma} \]Where:- $ Z $ = Z-score corresponding to 0.90 (top 10%)- $ \mu $ = mean expenditure ($95)- $ \sigma $ = standard deviation ($20)\[ 1.28 = \frac{X - 95}{20} \]3. **Solve for X**:\[ X - 95 = 1.28 \times 20 \]\[ X - 95 = 25.6 \]\[ X = 95 + 25.6 \]\[ X = 120.6 \]Therefore, to ensure that only the top 10% of customers receive a free gift, the supermarket should set the expenditure threshold above $120.60.---This analysis can be utilized by educational institutions to demonstrate practical applications of normal distribution and Z-scores in promotional and business policy planning.

Obtain the amount above for which customer would receive a free gift. The amount above for which…

Answered: The management of a supermarket want to…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Similar questions

If the average low temperature of a winter month in Rochester, NY is 18∘18∘ and the standard deviation is 3.4∘3.4∘, then according to Chebyshev's theorem, the percentage of average low temperatures in Rochester, NY between 12.56∘12.56∘ and 23.44∘23.44∘ is at least %.
Suppose Professor Alpha and Professor Omega each teach Introductory Biology. You need to decide which professor to take the class from and have just completed your Introductory Statistics course. Records obtained from past students indicate that students in Professor Alpha's class have a mean score of 80% with a standard deviation of 5%, while past students in Professor Omega's Class have a mean score of 80% with a standard deviation of 10%. Decide which instructor to take for Introductory Biology using a statistical argument.
In preparation for the upcoming school year, a teacher looks at raw test scores on the statewide standardized test for the students in her class. Instead of looking at the scores relative to the norms in the state, the teacher wants to understand the scores relative to the students who will be in the class. To do so, she decides to convert the test scores into z-scores relative to the mean and standard deviation of the students in the class. The mean test score in her upcoming class is 49, and the standard deviation is 20.7. The teacher now wants to identify those students who may need extra help. She decides to look at students who have z-scores below z = -2.00 Identify the test score corresponding to a z-score of below z = -2.00. Round to the nearest whole number.
Suppose that Jett achieves a score of 1250 on the SAT, and his sister Kate scores 29 on the ACT. The SAT scores are normally distributed with a mean of 1100 and standard deviation of 250. The ACT scores are normally distributed with a mean of about 20 and standard deviation of 5. Who did better, relative to their peers?
You hypothesize that people in stats classes are happier than people in all other classes. You compare happiness scores in three of your classes: Statistics, Developmental Psychology, and Social Psychology. In Statistics there are 15 students and the mean happiness rating is 23.1 with a standard deviation of 9.78. In Developmental Psychology there are 15 students and the mean happiness rating is 24.4 with a standard deviation of 2.92. In Social Psychology there are 15 students with a mean rating of 17.7 and standard deviation of 8.46. The sum of squares between groups is equal to 384. The sum of squares within groups is equal to 2461. Use the One-Way ANOVA calculation table to help calculate. What is the degrees of freedom between samples?
You hypothesize that people in stats classes are happier than people in all other classes. You compare happiness scores in three of your classes: Statistics, Developmental Psychology, and Social Psychology. In Statistics there are 15 students and the mean happiness rating is 23.1 with a standard deviation of 9.78. In Developmental Psychology there are 15 students and the mean happiness rating is 24.4 with a standard deviation of 2.92. In Social Psychology there are 15 students with a mean rating of 17.7 and standard deviation of 8.46. The sum of squares between groups is equal to 384. The sum of squares within groups is equal to 2461. Use the One-Way ANOVA calculation table to help calculate. What is the degrees of freedom within samples?
John finds that there is a scholarship available to all persons scoring in the top 5 % on the ACT test. If the mean score on the ACT is 21 with a standard deviation of 4.7, what score does he need in order to qualify for the scholarship?
Miranda and Karla began arguing about who did better on their tests, but they couldn't decide who did better given that they took different tests. Miranda took a test in Social Studies and earned a 71.4, and Karla took a test in Art History and earned a 60.9. Use the fact that all the students' test grades in the Social Studies class had a mean of 75.3 and a standard deviation of 10.7, and all the students' test grades in Art History had a mean of 66.4 and a standard deviation of 10.3 to answer the following questions.a) Calculate the z-score for Miranda's test grade.z=b) Calculate the z-score for Karla's test grade.z=c) Which person did relatively better? Miranda Karla They did equally well.
Lloyd and Tara began arguing about who did better on their tests, but they couldn't decide who did better given that they took different tests. Lloyd took a test in Social Studies and earned a 77.1, and Tara took a test in Math and earned a 66.4. Use the fact that all the students' test grades in the Social Studies class had a mean of 75.5 and a standard deviation of 10.5, and all the students' test grades in Math had a mean of 65.3 and a standard deviation of 8.8 to answer the following questions.a) Calculate the z-score for Lloyd's test grade.�=b) Calculate the z-score for Tara's test grade.�=c) Which person did relatively better? Lloyd Tara They did equally well.
An insurance company wants to make sure that its best customers (those with lowest value of insurance claims) stay with the company. To achieve this goal, the company plans to offer a 10% discount on the annual health insurance premium for customers with the lowest 20% of annual health care expenses. If the average annual health care expenses for a family of four is $3,650 with a standard deviation of $975, what is the amount of the maximum annual health care expense that will qualify for the proposed discount?
Lucille, Rocio, and Cristina are all taking College Mathematics but from different professors. They all recently took a statistics exam and the exam scores were normally distributed in each of their classes. • Lucille's class had an average grade of 78 and the standard deviation was 7. Lucille earned 83.95 on the exam. • Rocio's class had an average grade of 82 and the standard deviation was 3. Rocio earned 86.5 on the exam. • Cristina's class had an average grade of 76 and the standard deviation was 4. Cristina earmed 82.8 on the exam. Since some professors give harder exams than others, these students decided to use statistics to figure out who did the best on their exam. Use the Cumulative Z-Score Table to answer the following questions. Write your answers as a percent with two decimal places. Hint • Lucille's score places her above % of her class. • Rocio's score places her above % of her class. • Cristina's score places her above % of her class.
The board of examiners that administers the real estate broker’s examination in a certain state found that the mean score on the test was 450 and the standard deviation was 50. If the board wants to set the passing scores so that only the top 5% of all applicants pass, what should the passing score be? Assume that the scores are normally distributed.

SEE MORE QUESTIONS

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

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