Questions a-c are already completed just need d-f completed! thanks :) # Educational Exercise on Probability and Statistics**Exam Context:**The final exam in a sociology class consists of 100 multiple-choice questions. Each question has 6 possible answers, with only 1 correct option. An unprepared student makes random guesses for all answers.**Objective:**Analyze the statistical likelihood of obtaining correct answers using probability.---### Exercise Tasks:**a) Mean and Standard Deviation Calculation**- **Task:** Find the mean and standard deviation for the number of correct answers. Provide all formulas used.- **Instructions:** - Use the binomial probability formula, where the probability of success ($p$) is $1/6$, and the number of trials ($n$) is 100. - Formula for mean ($\mu$): $\mu = n \cdot p$ - Formula for standard deviation ($\sigma$): $\sigma = \sqrt{n \cdot p \cdot (1-p)}$**b) Probability Calculation**- **Task:** Find the probability of obtaining exactly 10 correct answers.- **Instructions:** - Use the binomial probability formula: \[ P(X=k) = \binom{n}{k} \cdot p^k \cdot (1-p)^{n-k} \] where $k = 10$.**c) Analyzing Unusual Outcomes**- **Task:** Determine if it would be unusual for a student to get 10 answers correct. Use a sentence and probability to justify your answer.- **Instructions:** - Calculate the probability from part (b). - Discuss what makes an event "unusual" in probability terms, often addressing whether the probability is below a certain threshold (e.g., 0.05).### Note:Use appropriate statistical tools or software for precise computation, rounding all answers to 4 decimal places. Ensure your explanations are clear to support fellow students’ understanding. d) Find the probability of obtaining less than 15 correct questions.e) Would the Normal Approximation produce accurate results? Provide all formulas used.f) Evaluate the probability of obtaining 20 correct questions by using the normal approximation.

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Description: Questions a-c are already completed just need d-f completed! thanks :) # Educational Exercise on Probability and Statistics**Exam Context:**The final exam in a sociology class consists of 100 multiple-choice questions. Each question has 6 possible an

Given Total number of questions n=100The total number of choices for each question =6The probability…

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d) Find the probability of obtaining less than 15 correct questions. e) Would the Normal Approximation produced accurate results? Provide all formulas used. f) Evaluate the probability of obtaining 20 correct questions by using the normal approximation.

d) Find the probability of obtaining less than 15 correct questions. e) Would the Normal Approximation produced accurate results? Provide all formulas used. f) Evaluate the probability of obtaining 20 correct questions by using the normal approximation.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Questions a-c are already completed just need d-f completed! thanks :)

d) Find the probability of obtaining less than 15 correct questions.

e) Would the Normal Approximation produce accurate results? Provide all formulas used.

f) Evaluate the probability of obtaining 20 correct questions by using the normal approximation.

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