Stats Professor Exam 5

Directions: Try to take the exam as if it were an actual test.  When you finish, click the problems one-by-one to check your answers.  There is a view answer link to just see the text solution, but if you got the problem wrong, you should watch the included video as well. 

1.  Below is a probability for the number of free throw attempts made by a NBA star out of 6 attempts:

What is the probability he makes 5 or more of his attempts?

2. In a game you pay $5, to have a 45/47 probability of losing your $5 and a 2/47 probability of winning $200 (you do not get your original $5 back).  What is your expected value for this game if you decide to play?

3.  A bin at a local big box store has 120 discounted packs of batteries of which 9 are old and contain batteries that no longer work.  If three of the packs of batteries are randomly selected for purchase, what is the probability that all of the packs of batteries are good ones (treat this problem as if it involves selection with replacement since 3/120 is less than 5%)?

4. A book bag contains three blue pens, two black pens, and one red pen.  If one pen is to be randomly selected from the bag, what is the chance it will end up being the red pen? If this happens to the owner of the bag, is he unusually unlucky to get the one unacceptable color for school work?

5. A marksman is able to hit the bull's-eye 92% of the time. If he shoots 10 times, what is the probability that he gets exactly 4 bull's-eyes? Assume each shot is independent of the others.

6. A pack of sunflower seeds (the kind for planting) contains 47 seeds that will germinate and 3 that will not germinate.  What is the probability that after a person chooses three seeds at random from the pack to plant, all three seeds eventually germinate?

7. A person rolls a fair six sided dice.  Find the probability the person rolls a one or a two.

8. The table below shows the incidence of heart disease among people who engage in different levels of alcohol consumption:

Find the probability that one randomly selected subject has heart disease or drinks less than 7 drinks per week.

9. If 11% of the population has a certain illness, what is the probability that among ten randomly chosen subjects at least one has the illness?

10.  In the math degree at FIU, a student must pick three elective courses among a set of 15 possible courses.  How many unique ways can a student meet his/her elective requirement?

11. The unemployment rate is around 9%.  What is the average number of people who will be unemployed if you randomly select groups of 30 people?

12. If 95% of the people diagnosed early with skin cancer survive, what is the standard deviation for the number of people who will survive when groups of 100 people from the population of people with early detected cancer are selected?

13. Is the following a binomial experiment?  Taking random guesses for the questions on a multiple choice exam with 20 questions where there are seventeen questions with five answer choices and 3 true/false questions with only two answer options (namely T/F).

14. Which of the following values cannot be probabilities? 1/3, 4/3, 0.989, 0.105, 1.10, √2 , √0.7 , -1/3

15. We know from poll data that only around 61% of eligible voters vote in presidential elections.  If we randomly select groups of 2,300 eligible voters and ask them if they voted in the last presidential election, would it be unusual to have 1,520 people say that they voted?

16. The table below shows the incidence of heart disease among people who engage in different levels of alcohol consumption:

Find the probability that one randomly selected subject has heart disease given that they drink more than 7 drinks per week.

17. A certain statistics class has only two kinds of majors who take the course: biology and psychology.  This class requires a group project.  The groups consist of two students only.  If one of these courses has 27 psychology majors and 23 biology majors, what is the probability that two randomly selected students that get paired together are both from the same major?   

18.  If 11% of the population has a certain illness, what is the probability that among ten randomly chosen subjects at least two of them have the illness?