- Final Solved Questions & Study Guide (Spring 2026)

STA-202 Applied Statistics Final Exam Solved Questions — Semester Summer 2025 (Retake)

Introduction

Applied Statistics (STA-202) is a core course in the BBA program at Daffodil International University (DIU), designed to equip students with essential data analysis skills for business decision-making. This course covers probability distributions, hypothesis testing, confidence intervals, and statistical inference—key tools for interpreting real-world business data. Whether you're preparing for a career in finance, marketing, or operations, mastering these concepts will help you analyze trends, validate assumptions, and make data-driven decisions.

For DIU BBA students, practicing past exam questions is one of the most effective ways to prepare for finals. This solved guide for the Summer 2025 Retake Final Exam provides step-by-step solutions to every question, ensuring you understand the logic behind each answer. By working through these problems, you’ll reinforce your grasp of Poisson distributions, normal curves, confidence intervals, and hypothesis testing—topics that frequently appear in exams and professional settings.

Exam Overview & Mark Distribution

This STA-202 Final Exam (Retake) consists of 5 questions worth a total of 40 marks, covering key topics from the syllabus. The exam tests both theoretical understanding and practical application of statistical methods. Here’s the breakdown:

• Question 1 (8 marks): Poisson distribution (conditions + calculation)
• Question 2 (8 marks): Normal distribution (characteristics + probability calculations)
• Question 3 (6 marks): Point vs. interval estimates + confidence interval construction
• Question 4 (6 marks): Degrees of freedom in t-distribution + confidence interval
• Question 5 (12 marks): Hypothesis testing steps (truncated in OCR)

Solved Questions

Question 1: Poisson Distribution

a) Explain the conditions that must be satisfied to apply the Poisson probability distribution.

• Events occur independently: The occurrence of one event does not affect the probability of another (e.g., customer complaints on different days).
• Constant average rate (λ): The mean number of events in a fixed interval remains stable (e.g., 9.7 complaints per day).
• Events occur one at a time: The probability of two events happening simultaneously is negligible.
• Rare events: The Poisson distribution approximates the binomial distribution when n is large and p is small (λ = np).

b) A commuter airline receives an average of 9.7 complaints per day. Using the Poisson formula, find the probability that on a certain day this airline will receive at most 4 complaints. Also, find the Mean and Standard Deviation.

Steps:

1. Poisson formula: \( P(X = k) = \frac{e^{-\lambda} \lambda^k}{k!} \), where \( \lambda = 9.7 \).
2. Calculate \( P(X \leq 4) \): Sum probabilities for \( k = 0 \) to \( 4 \):

- \( P(X=0) = \frac{e^{-9.7} \cdot 9.7^0}{0!} = 0.000061 \)

- \( P(X=1) = \frac{e^{-9.7} \cdot 9.7^1}{1!} = 0.000592 \)

- \( P(X=2) = \frac{e^{-9.7} \cdot 9.7^2}{2!} = 0.00287 \)

- \( P(X=3) = \frac{e^{-9.7} \cdot 9.7^3}{3!} = 0.00928 \)

- \( P(X=4) = \frac{e^{-9.7} \cdot 9.7^4}{4!} = 0.0225 \)

1. Sum probabilities: \( 0.000061 + 0.000592 + 0.00287 + 0.00928 + 0.0225 = 0.0353 \).
2. Mean (μ) = λ = 9.7 (given).
3. Standard Deviation (σ) = √λ = √9.7 ≈ 3.11.

Answer:

• Probability (at most 4 complaints) = 0.0353 (or 3.53%).
• Mean = 9.7, Standard Deviation = 3.11.

Question 2: Normal Distribution

a) Briefly explain the main characteristics of a normal distribution. Illustrate with the help of graphs.

Characteristics:

• Bell-shaped and symmetric: The curve is unimodal and centered around the mean (μ).
• Mean = Median = Mode: All three measures of central tendency coincide.
• Asymptotic tails: The curve approaches but never touches the x-axis.
• Empirical Rule: ~68% of data falls within 1σ, ~95% within 2σ, and ~99.7% within 3σ.
• Defined by μ and σ: The shape changes with the mean (location) and standard deviation (spread).

Graph Illustration:

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