| Course | BU 321 Business Statistics |
|---|---|
| Unit | Unit 2 |
| Paper type | Distribution problem set |
| Length | About 1,130 words, 7 pages |
| Format | APA 7 student paper |
| School | Herzing University |
| Program | BS in Business Management |
| Updated | September 2026 |
Free sample paper for BU 321 Unit 2
Friday Night at a Pizza Counter, in Three Distributions: A Worked Problem Set on Binomial, Poisson and Normal Questions for a Composite Delivery Chain
Student Name
Business, Herzing University
BU 321: Business Statistics
Instructor Name
February 4, 2026
Friday Night at a Pizza Counter, in Three Distributions: A Worked Problem Set on Binomial, Poisson and Normal Questions for a Composite Delivery Chain
This problem set answers six probability questions about one composite business, Brickoven Express, the invented Columbus pizza delivery business whose order data were described in Unit 1. Each answer carries three parts: the distribution the situation calls for and the conditions that make it fit, the calculation set out so it can be reproduced, and a sentence a store manager could act on. Calculations were done in Python; where a spreadsheet function would give the same result, the equivalent Excel function and its arguments are named. Probabilities are rounded to four decimal places, and answers are stated as percentages where that reads more naturally.
Question 1: All Twelve Orders on Time
Situation: During the busiest half hour of a Friday dinner rush, the Eastgate store dispatches 12 orders. In the sample described in Unit 1, 90.4 percent of orders arrived within the 35-minute promise, so this question uses 0.90 as the probability that any one order arrives on time. What is the probability that all 12 arrive on time?
Distribution: binomial. The conditions are a fixed number of trials (12 orders), two outcomes for each (on time or late), the same probability of success on each trial (0.90) and independence between trials (Anderson et al., 2020). Independence is the weakest assumption here, since orders dispatched in the same rush share traffic and weather, so the answer should be read as an approximation.
Parameters: n = 12, p = 0.90. Calculation: P(X = 12) = 0.90 raised to the 12th power = 0.2824. Excel: BINOM.DIST(12, 12, 0.9, FALSE).
Answer for the manager: there is only about a 28 percent chance that every one of the 12 rush orders arrives on time, so on a typical busy Friday at least one late order should be expected, and staff should be ready to handle it.
Question 2: Two or More Late
Situation: Using the same 12 orders, what is the probability that two or more arrive late?
Distribution: binomial, with the same conditions as Question 1. Two or more late means ten or fewer on time. It is easier to compute the complement: the probability of zero late or exactly one late.
Calculation: P(0 late) = 0.2824. P(exactly 1 late) = 12 times 0.10 times 0.90 raised to the 11th power = 0.3766. P(2 or more late) = 1 minus 0.2824 minus 0.3766 = 0.3410. Excel: 1 minus BINOM.DIST(10, 12, 0.9, TRUE) gives the probability of 11 or 12 on time subtracted from 1, which is the same result.
Answer for the manager: about one Friday rush in three would see two or more late orders among the first 12. If the store offers a coupon for each late order, it should budget for that frequency rather than treating multiple late orders as unusual.
Question 3: A Very Busy Quarter Hour
Situation: The chain's point-of-sale records show that during Friday dinner, the Eastgate store receives an average of 5.5 orders per 15-minute interval. The store's kitchen can prepare about 8 orders in 15 minutes before tickets start to back up. What is the probability that 9 or more orders arrive in a given 15-minute interval?
Distribution: Poisson. The situation counts events in a fixed interval, orders arrive one at a time, the average rate is steady within the dinner period and one order's arrival does not affect another's (National Institute of Standards and Technology, 2012; Ross, 2014). The rate is not steady across the whole evening, so the model applies only within the peak period.
Parameter: lambda = 5.5. Calculation: P(X of 9 or more) = 1 minus the sum of P(X = k) for k = 0 to 8, where P(X = k) = e to the power of minus 5.5, times 5.5 to the power k, divided by k factorial. The result is 0.1056. Excel: 1 minus POISSON.DIST(8, 5.5, TRUE).
Answer for the manager: roughly one in every nine or ten Friday dinner intervals will bring more orders than the kitchen can prepare in time. Over a two-hour dinner rush with eight intervals, at least one overload is more likely than not, which supports having a prep cook start early on Fridays.
Question 4: A Slow Quarter Hour
Situation: With the same average of 5.5 orders per interval, what is the probability that 3 or fewer orders arrive in a 15-minute interval, time a manager could use for cleanup or restocking?
Calculation: P(X of 3 or fewer) = P(0) + P(1) + P(2) + P(3) = 0.2017. Excel: POISSON.DIST(3, 5.5, TRUE). The probability of no orders at all is only 0.0041.
Answer for the manager: about one Friday dinner interval in five is quiet enough for side work, but a completely empty interval is very rare, so restocking should be planned in short bursts rather than in a single block.
Question 5: Deliveries Over 35 Minutes
Situation: Delivery times in the Unit 1 sample had a mean of 24.6 minutes and a standard deviation of 8.25 minutes. If delivery times are approximately normal, what proportion of deliveries would exceed the 35-minute promise?
Distribution: normal. Delivery time is a continuous measure, and its sample distribution is mound shaped with a skewness of 0.48, close enough to symmetric for a normal approximation, though the slight right tail means the model may understate very long deliveries.
Calculation: z = (35 minus 24.6) divided by 8.25 = 1.26. P(Z greater than 1.26) is about 0.104; using the unrounded mean and standard deviation from the data gives 0.1042. Excel: 1 minus NORM.DIST(35, 24.6, 8.25, TRUE).
Answer for the manager: the model predicts that about 10.4 percent of deliveries run past 35 minutes, very close to the 9.6 percent actually observed in the sample. The agreement suggests the normal model is a reasonable planning tool for this chain.
Question 6: When the Normal Model Is the Wrong Choice
Situation: A manager asks for the probability that a delivery takes less than 5 minutes.
Answer: the normal model gives z = (5 minus 24.6) divided by 8.25 = minus 2.38, and a probability of about 0.009, which would suggest that nearly one delivery in a hundred arrives in under 5 minutes. No delivery in the sample took less than 9 minutes, and driving, parking and handing over an order take several minutes even for the nearest customers. A normal curve extends in both directions without limit, but delivery times cannot. This is a case where the model's assumptions fail at the edge of the data, and the answer for the manager is that the normal model should not be used for questions far below the observed minimum. The observed data, not the model, answer this question: essentially zero.
References
Anderson, D. R., Sweeney, D. J., Williams, T. A., Camm, J. D., & Cochran, J. J. (2020). Statistics for business and economics (14th ed.). Cengage.
National Institute of Standards and Technology. (2012). NIST/SEMATECH e-handbook of statistical methods. https://www.itl.nist.gov/div898/handbook/
Ross, S. M. (2014). Introduction to probability models (11th ed.). Academic Press.
Reading the BU 321 Unit 2 instructions
The Unit 2 problem set asks you to solve probability questions using the distributions covered in the course, usually the binomial, Poisson and normal. Most versions supply a scenario or dataset and a list of questions. For full credit, each answer should name the distribution, explain why the situation fits it, show the parameters and the calculation, and interpret the result in business terms. Many instructors accept spreadsheet functions if the function name and arguments are reported. Numbering should match the questions, and rounding should be consistent. Although the assignment is a problem set rather than an essay, cite the textbook for definitions and any outside source in APA 7.
How the BU 321 Unit 2 example is put together
The sample numbers six questions under one scenario. Questions 1 and 2 use the binomial distribution for 12 rush-hour orders with a 0.90 on-time probability, finding a 28 percent chance of all on time and a 34 percent chance of two or more late. Questions 3 and 4 use a Poisson rate of 5.5 orders per quarter hour to find how often the kitchen is overloaded or quiet. Question 5 uses the normal distribution with the sample's mean and standard deviation and compares the prediction with the observed share. Question 6 explains why the normal model gives a nonsensical answer for very short deliveries. Every item ends with a manager's sentence.
Where the points sit in the BU 321 Unit 2 rubric
The rubric for the problem set typically assesses selection of the distribution, correct setup and calculation, interpretation and presentation. Selection earns full points when the conditions for the distribution are stated and checked, not just named. Setup and calculation are judged by correct parameters, a reproducible method and accurate results, whether computed by hand or with a named function. Interpretation rewards a sentence that turns each probability into a decision or expectation, as the sample does with coupon budgets and prep staffing. Instructors increasingly give credit for recognizing when a model does not fit, which is why the final question is valuable. Clear numbering and consistent rounding support presentation.
Common BU 321 Unit 2 mistakes, and how to avoid them
A frequent Unit 2 mistake is choosing a distribution by habit, using the normal curve for counts or the binomial when trials are not fixed. Another is giving a bare number without saying what it means. Students often skip the conditions, especially independence, which is the weakest assumption in many business scenarios. Some show a spreadsheet result with no function or arguments, so the instructor cannot check it. Rounding too early can shift answers noticeably. Finally, test your model against the data when you can; the sample compares the normal prediction with the observed share of late deliveries, which is a simple check that many students never make. Keep each answer self-contained, so a reader who jumps to one question can follow it without the others.
Get a BU 321 Unit 2 example written to your instructions
Send the Unit 2 instructions and the rubric from your BU 321 classroom, with the scenario and any data file the assignment provides. We write a custom example that names each distribution and its conditions, labels the parameters, shows reproducible working and ends every item in plain business language. First custom sample free, back in 24 to 48 hours.
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BU 321 Unit 2 questions, answered
Do I have to show the formula if I used a spreadsheet?
Most sections want the function and its arguments recorded even where the algebra is not required, because that is what makes a result checkable. Write the function you called and what you passed to it, and say which cell or range held the data. If your instructions ask for hand working as well, show the substitution rather than only the final figure.
How much rounding is acceptable?
Carry full precision through the calculation and round once at the end, to whatever the instructions specify. Rounding an intermediate value and then continuing is the quiet source of answers that come close without being right, and a marker comparing against their own working will see the drift. State the rounding you used in a line.
When is the normal distribution the wrong choice?
Whenever the quantity is a count and the conditions of a counting model are met, among other cases your reading will list. The test is the situation rather than convenience: fixed trials with two outcomes, occurrences in an interval, and a continuous measurement all point toward different models. Name the conditions you checked before you calculated anything.
Where can I find a free BU 321 Unit 2 sample paper?
The complete BU 321 Unit 2 problem set, all six questions with calculations and manager sentences, is shown above for free. For your own scenario or question list, share the assignment and a worked set will be written to it without charge, typically in 24 to 48 hours.
Can I use Excel functions in BU 321 Unit 2?
Most instructors allow it if you report the function and its arguments. The sample names the Excel equivalent for every calculation, such as BINOM.DIST or POISSON.DIST, so each result can be reproduced. Show at least one formula by hand if your rubric asks for it.