In: Statistics and Probability
1. In Spring 2019, a local community college decided to switch textbooks for their calculus courses. In order to compare how students fared with the new book compared to the old book, a professor recorded the average grades that the students received on their exams. The average exam scores of 17 randomly selected students are shown below. State the 5-number summary by clearly labeling each value and create a boxplot for this data.
62.9 |
73.80 |
98.5 |
76.2 |
81.5 |
67.8 |
72.2 |
59.8 |
80.2 |
85.5 |
49.6 |
82.65 |
72.2 |
61.2 |
85.2 |
78.8 |
37.3 |
4. A statistics professor gave a final exam to his students where the first page consisted entirely of 12 true/false questions. Assume that a student decided to randomly guess on all 12 true/false questions on the first page. Use this data to answer the following questions.
Find the probability that this student guesses all 12 correctly
Find the probability that this student guesses at least 6 correctly
Find the probability that this student guesses exactly 7 correctly
Find the probability that this student guesses between 5 and 10 questions correctly.
Find the probability that this student guesses no more than 10 questions correctly.
1. 5-number summary table
Minimum | 1st Quartile | Median | 3rd Quartile | Maximum |
37.3 | 62.9 | 73.8 | 81.5 | 98.5 |
4.
It is given that a professor gave his student a 12 questions test. That is, the size of the sample of the questions is n = 12. The 12 questions may be considered as 12 independent trials.
Consider the event of answering the question correctly as a “success”. All the 12 questions in the exam are true/false questions and the student answers them randomly. Thus, the probability that the answer of the student is correct that is, the probability of success in each trial is p = 1/2. Then q = 1 – (1/2) = 1/2.
Consider X as the number of questions answered correctly among the 12 questions. Then, X has a Binomial distribution with parameters (n = 12, p = 1/2) with pdf as given below:
P(x) = 12Cx*(1/2)x* (1/2)12–x ; x = 0, 1 , 2 , ...,12.
Find the probability that this student guesses all 12 correctly
P(X = 12) = 0.0002441406
Find the probability that this student guesses at least 6 correctly
P(X >= 06) = 0.8066406
Find the probability that this student guesses exactly 7 correctly
P(X = 07) = 0.1933594
Find the probability that this student guesses between 5 and 10 questions correctly
P(5 < X < 10) = 0.5935059
Find the probability that this student guesses no more than 10 questions correctly
P(X < 11) = 0.9968262