Break-even Analysis and Probability Calculations in Statistics Course

This assignment provides solutions to problems involving break-even analysis and probability calculations. It includes calculations for break-even points in different scenarios, such as determining the number of people needed to break even for a seminar and the number of students required to break even in a course. The assignment also explores probability concepts, including calculating the probabilities of different numbers of arrivals per day and determining the expected time between arrivals and the variance of the time between arrivals. The solutions are presented with detailed calculations and formulas, demonstrating the application of these concepts in statistics.

Chapter 1 - Problem 22
The calculation of number of people needed by Golden Age to break even is as shown below:
Since, people cannot be 44.24 hence, at least 45 people must attend each seminar so that the
break even condition met.
Chapter 1 - Problem 23
(a) The calculation of number of students needed to break even is as shown below:
Therefore, 19 students must enrol so that the break even condition met.

(b) The calculation of number of students needed to break even when smaller room
possibility is considered is as shown below:
Therefore, 14 students must enrol so that the break even condition met.
Chapter 2- Problem 43
(a) The calculation of probability of exactly 0, 1, 2, 3, 4, and 5 arrivals per day in Excel is as
shown below:

(b)
The sum of these probabilities in Excel is calculated as follows:
This sum is less than 1 because arrivals more than 5 also have some probabilities associated
with them. The sum of all the probabilities from zero to infinity arrivals will be equal to 1.
Chapter 2 - Problem 45
(a) The formula to calculate the expected time between arrivals is as written below:
The calculation in Excel is as shown below:

Therefore, the expected time between arrivals is 0.33 hours or it can be also written as:
(b) The formula to calculate the variance of the time between arrivals is as written below:
The calculation of variance in Excel is as shown below:
Therefore, the variance of the time between arrivals is 0.11 hours or it can be also written as: