Statistics & Probability Model - Relevant Random Variable - Marketing Assignment Help

Assignment Task :

1. The marketing division of the beverage company wants to conduct a survey to gather information on customer satisfaction for its popular brand, Cola. The data on customer rating is obtained on a 3- point satisfaction scale, HS (Highly satisfied), S( Satisfied ), NS ( Not Satisfied ). Moreover, data on their age group L (<35 Years ) and M( ≥ 35 years is also recorded. The following data is collected on 20 randomly chosen respondents.  

1. Construct probability table for  “Age group “ and Satisfaction level”
2. What is the probability that the respondent who is “Satisfied” will belong to age group L? 
3. What proportion of the respondents would be “Highly satisfied? 
4. How likely a 50 years old respondent won’t be satisfied? 
5. Suppose a random variable is defined on the basis of the above data as a number of respondents who are “ Satisfied “ with the brand. Develop a probability model for the random variable.  
6. Using the probability model, calculate the probability that at least three customers will be “Satisfied”?  
The Survey is conducted in a shopping mall where the interviewer is standing at the entrance and record the number of footfalls per minute. After conducting such an interview for three months, the interviewer finds that’s the data follows a Poisson distribution with mean 2 per minute.  
7. Define the relevant random variable which follows the Poisson distribution. What is the mean and standard deviation of the distribution? 
8. Find the probability the number of footfalls on a weekday between 11:30 – 11:31 am will be 4 9. Find the probability that at least 2 footfalls will be recorded between 7:00-7:05 pm  

2. The analytics division of the manufacturer of cola dispensing machine assumes that the life expectancy of the dispensing machine is normally distributed with a mean life of five years and a standard deviation of eight months. 

• What is the probability that a randomly selected dispensing machine will be in working condition for more than six years?  
• The manufacturing company has a three – year warranty period on the dispensing machines. What percentage of their machines will be in operating condition after the warranty period?  
•   Ninety- five percent of the machines will have a life expectancy of at least how many months?

3. The manufacturer of the cola dispensing machine wants to estimate the meantime to repair a particular fault in the machine. Sixteen machines with the same fault are chosen at random from the company’s records and the mean repair time is found to be 96 mins with standard deviation 10 mins.  
Compute 95% confidence interval for the mean repair time.  
Stating hypotheses, test at a suitable level of significance; whether or not the meantime to repair is 98 mins. Obtain the p-value of the test.  
 

4. The analytics division of the firm believes that the rupee spent on advertising, the price of the brand, and the number of retail stores selling the brand in a particular month influences the sales of cola. The company collects weekly data on sales of 500 ml bottles of Cola for the last five years. The sales are in thousands of units per week, the advertising is given in thousands of rupees per week, and the price is the unit retail price for the particular week. The following outputs are obtained.

• Write down the estimated multiple regression equation. 
• Interpret estimated regression coefficients.  
• Interpret the p- values  
• Interpret R-Sq and adjusted R-Sq and their difference.  
• How do you interpret Residual Standard Error? 
• Based on the multiple regression model given above, estimate the monthly sales, if the company spends INR 40000 on advertising, the price of one 500 bottle of Cola is INR 40, and the item is being sold at 3 retail stores.  

5. A beverage company wants to adopt a new marketing strategy to increase the market share of its key product “Cola”. The marketing manager wants to explore the data that he has collected recently from 200 markets before taking any decision. The weekly data on sales (in ‘000’ of units) is collected for 200 ml and 500ml bottles of the product “Cola”. Some of the descriptive statistics of sales data for both the variants along with graphs are furnished below.  

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