Please show all your work. Thank you! 4. John is considering taking Engineering

Question

Please show all your work. Thank you!

4. John is considering taking Engineering Statistics for the next semester, His decision would depend on the possible grade he could get in the course. Based on his knowledge of and linear algebra, he is making an assumption: there is a 0.2 a D 0.22 chance that he will get (GPA 1), chance that he will get a c (GPA-2).0.5 chance that he will get a B (GPA 3) and a 0.1 chance that he will get an A (GPA-4). a. Let x denote the GPA that John would get in Engineering Statistics I. What is the cumulative distribution function F(x) for all possible values of X? b. What is the probability that John get at least a 2.5 GPA out of this class? c. Suppose before taking this class, John has an average GPA of 2.5. He would bope to use this class to improve his average GPA. Should he take the course? d. Assume John has another option to take Simulation I that has an expected GPA of 2.7 with a standard deviation of 2. Which class should he choose? Why? 5. Conduct a "Roll the dice" experiment by yourself Roll a 6-sided dice 30 and website: down the number on the dice every time (if you do not have a dice, you can use the http://www.random,org/dice) distribution your experiment. a. Draw a probability mass function to describe the of b. What type of probability distribution do you think this experiment yielded?

Explanation / Answer

part a)

The cdf is as shown below:

part b)

P(x2.5) = P(x=3) + P(x=4)

P(x2.5) = 0.5 + 0.1 = 0.6

.

part c)

Since Grades B and A are more likely (p = 0.6) , thus John must go for the class, as it will have higher chances of reach grades A and B, which are more likely.

.

Grade D C B A PMF f(x) 0.2 0.2 0.5 0.1 CDF F(x) 0.2 0.4 0.9 1

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