Podcast
Questions and Answers
What is the standard error of the sampling distribution of the average tip received from 15 customers?
What is the standard error of the sampling distribution of the average tip received from 15 customers?
Why can the Central Limit Theorem (CLT) be applied when calculating the distribution of the average tip from 55 customers?
Why can the Central Limit Theorem (CLT) be applied when calculating the distribution of the average tip from 55 customers?
What is the probability that the average tip received from 55 customers is between ₹110 and ₹140?
What is the probability that the average tip received from 55 customers is between ₹110 and ₹140?
How is the expectation of the daily expenditure at Café Kamla determined?
How is the expectation of the daily expenditure at Café Kamla determined?
Signup and view all the answers
What is the variance of the daily expenditure at Café Kamla?
What is the variance of the daily expenditure at Café Kamla?
Signup and view all the answers
Study Notes
ITC Narmada - Tip Distribution Analysis
- The tips from customers at ITC Narmada follow a right skewed distribution.
- Mean tip amount is ₹100 with a standard deviation of ₹25.
- For 15 customers:
- Mean of the sampling distribution equals the population mean: ₹100.
- Standard error calculated as ₹25/√15 = ₹6.45.
- Cannot assume normal distribution due to skewness and sample size being less than 30.
- For 55 customers:
- Average tip from 55 customers can be considered normally distributed.
- Mean remains ₹100, with standard error as ₹25/√55 ≈ ₹3.37.
- Probability calculations:
- Probability that average tip is between ₹110 and ₹140: P(110 ≤ X ≤ 140) results in a value of approximately 0.0015.
- Probability that average tip is at most ₹110: P(X ≤ 110) is approximately 0.9985.
Café Kamla - Daily Expenditure Analysis
- Daily expenditure at Café Kamla can be defined by the variable "X".
- The probability of visiting Café Kamla is 0.25, making it a Bernoulli trial.
- Expenditure distribution:
- X = ₹70 with a probability of 0.25.
- X = ₹0 with a probability of 0.75.
- Expectation (mean) and variance of daily expenditure to be calculated for X.
Additional Notes
- Central Limit Theorem (CLT) applies for sample sizes ≥ 30, allowing normal approximation of sampling distribution despite right skewness.
- Understanding sampling distributions and probabilities is crucial for insights into customer behavior and economic forecasting.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
This quiz focuses on problem-solving based on Chapters 3, 4, and 5 from the Quantitative Methods course notes. Work through the problems to enhance your understanding of the material covered in class, including real-world applications like tips distribution in a restaurant setting.
