Question

In: Statistics and Probability

Suppose that the probability of obtaining a particular grade in an undergraduate statistics course, is defined...

Suppose that the probability of obtaining a particular grade in an undergraduate statistics course, is defined by the following table:

grade A B C D F
probability .25 .35 .2 .15 .05

(a) Using the usual numerical values for the grades, define the corresponding random variable, X, and its probability mass function, p(x).

(b) Calculate P(X ≤ 2), P(X < 2), and P(X ≥ 3).

(c) Plot the cumulative distribution function F(x).

(d) Compute the mean µ = E(X).

Solutions

Expert Solution


Related Solutions

Good performance (obtaining a grade of A+) in this probability class depends on your attendance (A)...
Good performance (obtaining a grade of A+) in this probability class depends on your attendance (A) and completion of assignments (C). The probability that you will receive a grade of A+ are 95%, 75%, 50%, and 0%, if you attend the class and complete the assignments, if you attend but do not complete assignments, if you do not attend but complete assignments, and if you neither attend nor complete assignments, respectively. Further assume that if you attend the class, there...
The semester average grade for a statistics course is 76 with a standard deviation of 5.5....
The semester average grade for a statistics course is 76 with a standard deviation of 5.5. Assume that stats grades have a bell-shaped distribution and use the empirical rule to answer the following questions (explain your responses with the help of a graph): 1. What is the probability of a student’s stat grade being greater than 87? 2. What percentage of students has stat grades between 70.5 and 81.5? 3. What percentage of students has stat grades between 70.5 and...
It is thought that 12% of all students taking a particular course received a grade of...
It is thought that 12% of all students taking a particular course received a grade of A. In a sample of 155 students, it is found that 21 made an A. can we conclude that the ratio of students with grade of A is higher than 12%? To do so a) State the null and alternative hypotheses. b) Compute the test statistic-value. c) Find the critical-value. d) Identify the decision rule and express your decision.
Q25.If the records show that, the probability of failing (with grade F) this course is p,...
Q25.If the records show that, the probability of failing (with grade F) this course is p, what is the probability that at most 2 students out of 15 fail this course? {Hint: use binomial distribution} Q26.If the records show that, the probability for a student to get a grade B this course is p, what is the probability that exactly 4 students out of 15 will have a grade B for the course? {Hint: use binomial distribution} Q27.What is the...
The average grade in a statistics course has been 70 with a standard deviation of 8....
The average grade in a statistics course has been 70 with a standard deviation of 8. If a random sample of 51 is selected from this population, what is the probability that the average grade is more than 72? Use Appendix B.1 for the z-values. (Round your z-value to 2 decimal places and the final answer to 4 decimal places.) Probability
Normal distribution of Statistics course in Mechanical Engineering Department According to the grade point average is...
Normal distribution of Statistics course in Mechanical Engineering Department According to the grade point average is 50 and standard deviation is 3. Since the passing grade is 45: a) What is the percentage of probability of Mechanical Engineering students from the course? b) What is the probability that Mechanical Engineering students will pass the course? c) What is the grade of the student who gets a grade better than 90% of the class from the statistics course? d) What is...
Suppose that grade point averages of undergraduate students at one university have a bell-shaped distribution with...
Suppose that grade point averages of undergraduate students at one university have a bell-shaped distribution with a mean of 2.61 and a standard deviation of 0.39. Using the empirical rule, what percentage of the students have grade point averages that are between 1.83 and 3.39?
Suppose that grade point averages of undergraduate students at one university have a bell-shaped distribution with...
Suppose that grade point averages of undergraduate students at one university have a bell-shaped distribution with a mean of 2.612.61 and a standard deviation of 0.390.39. Using the empirical rule, what percentage of the students have grade point averages that are between 1.831.83 and 3.393.39?
Suppose that grade point averages of undergraduate students at one university have a bell-shaped distribution with...
Suppose that grade point averages of undergraduate students at one university have a bell-shaped distribution with a mean of 2.62 and a standard deviation of 0.43. Using the empirical rule, what percentage of the students have grade point averages that are at least 1.76? Please do not round your answer.
Suppose that grade point averages of undergraduate students at one university have a bell-shaped distribution with...
Suppose that grade point averages of undergraduate students at one university have a bell-shaped distribution with a mean of 2.52 and a standard deviation of 0.43. Using the empirical rule, what percentage of the students have grade point averages that are between 1.23 and 3.81?
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT