STA101: Discrete Probability Distributions Take Home Assignment 3

This document presents a comprehensive solution to a take-home assignment on discrete probability distributions. The assignment involves analyzing a statistics test scenario where a student guesses on all questions. The solution includes constructing a probability distribution table, calculating the expected number of incorrect answers using the formula E(X) = ΣXP(X), explaining the concept of expectation in statistics within the context of the test, determining the probability of achieving a certain score, and evaluating whether the student's actual score aligns with expectations. The analysis covers the binomial distribution and probability calculations, providing a detailed understanding of the concepts. This solution is available on Desklib, a platform offering various study resources for students.

Take Home Assignment 3
Discrete Probability Distributions
Mark is sitting a statistics test, which consists of 10 questions where each question has four
possibilities (A, B, C & D) but only one is correct. After the test, Mark told you he didn’t study for
the test at all and guessed all answers.
(a) If Mark guessed each and every item in the test, describe the probability distribution for the
number of correct guesses. Present the probability distribution in the form of a table using 4
decimal points in your answers. (Use Excel to calculate the probabilities.)
Answer
Number of questions correctly got Probability
0 0.0563
1 0.1877
2 0.2816
3 0.2503
4 0.1460
5 0.0584
6 0.0162
7 0.0031
8 0.0004
9 0.0000
10 0.0000
(b) Using the formula: E(X) = XP(X), find out the number of incorrect answers Mark would
expect to get. (You can use Excel to do the calculation. Just copy the Excel output onto your
Word document.)
Answer
E ( X ) =XP ( X )= ( 0∗0.0563 )+ (1∗0.1877 ) + ( 2∗0.2816 ) + ( 3∗0.2503 ) + ( 4∗0.1460 ) + ( 5∗0.0584 ) + ( 6∗0.0162 ) +
¿ 2.5
(c) What does expectation mean in statistics? Explain your answer in the context of the A to D
Test.
Answer
The expectation refers to a weighted average of the possible values that X can take. In this
case it implies that the weighted average of the possible values A to D is 2.5.
(d) What is the probability that Mark gets 8 or more correct answers for this test?
Answer
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P ( X ≥8 )=0.0004+ 0.0000+0.0000=0.0004
(e) When the result was released, Mark got 3 out of 10. Would you be surprised? Do you think
Mark lied to you? Explain your answer.
Answer
I would not be surprised with Marks results as this was expected. We calculated the
expectation to be 2.5 which is not very far from what Mark scored of 3 out of 10.
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