STATS MIDTERM EXAM 2

1.      A Professor in a research university wanted to know whether his teaching methods work in the real world. To acquire this information, the Professor surveyed the students of that university who took his course and determined whether each student took his course or not and whether a job was offered to the student in the real world. From the information developed, the Professor produced the table of joint probabilities below

What is the probability that a job offer was made by the industry in the real world to a student of this university?

2.      What is t distribution? What does it depend upon? 

3.      Probability that there is a natural disaster in our area is 0.03. The cause of university closings on regularly scheduled class-day can be natural disaster or other reasons. If there is natural disaster, the probability of university closure for the day is 0.90. If there is no natural disaster, the probability of university closure for the day is 0.02. Suppose you received a phone call at 4 AM in the morning that the university is closed on a regularly scheduled class day. What is the probability that there is a natural disaster in the happening in our area?

4.      In an exam students’ score summary statistics is as follows:
Number of students = 1000, Mean = 80, Median = 83, Std.Dev =8. Your score in the exam = 96

If the exam scores have a symmetric bell-shaped distribution, what can we say about the scores that fall between 64 and 96?

5.      How can you use t distribution to estimate population mean  from a sample mean? Provide an example.

6.      A dice is rolled  ( 6 faces: 1,2,3,4,5,6)  and a quarter is tossed, find the probability that the dice shows an odd number and the quarter shows a head.

7.      A Professor in a research university wanted to know whether his teaching methods work in the real world. To acquire this information, the Professor surveyed the students of that university who took his course and determined whether each student took his course or not and whether a job was offered to the student in the real world. From the information developed, the Professor produced the table of joint probabilities below:

Given that a student took his course, what is the probability that he/ she got a job offer?

8.      What is the standard deviation of the following number set :

1,1,1,1,1,1,1,1,1,1,1,1,1,1……………five million 1s

9.      An bag contains 6 red balls and 4 black balls. Three balls are drawn without replacement from the bag. What is the probability that all of the three balls are black?

10.  In an exam students’ score summary statistics is as follows:
Number of students = 1000, Mean = 80, Median = 83,, Std.Dev =8. Your score in the exam = 96

Assuming the distribution is normal and symmetrical, how many students scored below you?