Fall 2011 Exam Score: /76. Exam 2

Transcription

1 Math 12 Fall 2011 Name Exam Score: /76 Total Class Percent to Date Exam 2 For problems 1-8, circle the letter next to the response that BEST answers the question or completes the sentence. You do not have to show any work or write any explanations here. Make sure to read each statement carefully! each 1. The number 5! means A) 5? B) C) P D) n 5 2. The probability of an event is always A) greater than zero B) less than 1 C) between 0 and 1, inclusive D) greater than 1 3. For the probability distribution of a discrete random variable x, the sum of the probabilities of all values of x must be: A) equal to zero B) in the range zero to 1 C) equal to.5 D) equal to 1 3. Two complementary events A) taken together do not include all outcomes for an experiment B) taken together include all outcomes for an experiment C) can occur together D) are always independent 4. Two mutually exclusive events A) always occur together B) can sometimes occur together C) cannot occur together D) can occur together, provided one has already occurred

2 5. A conditional probability is a probability A) of a sample space based on a certain condition B) that an event will occur given that another event has already occurred C) that an event will occur based on the condition that no other event is being considered D) that an event will occur based on the condition that no other event has already occurred 6. Two events, A and B, are described in the Venn diagram below. A) A and B are mutually exclusive B) P(A and B) = 0 C) P(A or B) = P(A) + P(B) D) all of the above A B 7. The probability distribution table of a discrete random variable lists: A) the bottom half of the values that the random variable can assume and their corresponding probabilities B) all of the values that the random variable can assume and their corresponding probabilities C) all of the values that the random variable can assume and their corresponding frequencies D) the top half of the values that the random variable can assume and their corresponding frequencies For problems #8-17 you need to show work in order to receive credit! Where applicable, state which calculator program you are using and what parameters you are using for your calculations. State what you are finding, for example P( x < 6 ). 8. Find the total number of outcomes for 5 rolls of a 9-sided die. 9. My favorite ice-cream shop offers 30 flavors of ice-cream. After a long day of grading exams I want to buy a 3-scoop ice-cream cone, and I want three different flavors. How many ways are there to arrange my 3 scoops, if I do care in which order they are stacked? 10. A court randomly selects a jury of 4 persons from a group of 16 persons. How many ways are there to select such jury?

3 11. Suppose a person randomly guesses on all of the 8 multiple choice questions on this exam. Each of the problems has 4 choices. (a) In how many possible ways can the 8 questions be answered? (b) What is the probability that this person will answer all of them correctly? Round to 3 significant digits. 12. The social network Facebook is becoming more and more popular (has over 800 million users). 28% of the year old users check Facebook before even getting out of bed in the morning. Let x represent the number of people that check their Facebook before getting out of bed in the morning. Suppose two people in the age group years old are randomly selected. (a) Draw a tree diagram for this experiment, carefully labeling the tree with the outcomes and their probabilities. List all the final outcomes and calculate their probabilities. (b) Use the tree diagram to complete the probability distribution table for x. x P( x ) (c) Is this a binomial experiment? Explain why or why not.

4 13. A drug test was tested for its accuracy. The following table gives the two-way classification of 300 persons that took this drug test to determine whether or not they had used marijuana. Results from Tests for Marijuana Use Did the Subject Actually Use Marijuana? Positive test result (Test indicated that marijuana is present.) Negative test result (Test indicated that marijuana is absent.) Yes 119 (true positive) 3 (false negative) No 24 (false positive) 154 (true negative) (a) had used marijuana. (b) had not used marijuana OR had a negative test result. (c) gets a false positive result. That is, that she has not used marijuana AND that she had a positive test result. (d) will test positive, given that she did use marijuana. (e) Based on the probabilities in part (a) and (d), are the events "the person did use marijuana" and "the person test positive" independent? Explain why or why not. 1 pt

5 14. Suppose 15% of all households in the bay area are cat owners (a) If a random sample of 20 households in the bay area is selected, what is the probability that exactly 8 of them are cat owners? (b) If a random sample of 20 households in the bay area is selected, what is the probability that more than 8 of them are cat owners? (c) Let x represent the number of households in the bay area that are cat owners in a random sample of 20 households. Calculate and interpret the mean of x. 15. A study shows that girls who watch soap operas are more likely to have eating disorders. Suppose the study was based on a sample of 4000 girls, with r = 0.74, using the number of hours of soap opera watched per week as the independent variable, and the severity of the eating disorder (scale 1-10) as the dependent variable. Based on this research, can we conclude that watching soap operas causes eating disorders? Briefly explain why or why not? 16. The following is a printout from the Correlation Game that I have posted on my website. Match each of the four scatter plots to its r-value.

6 17. Listed below are the chest sizes (in inches) and weights (in pounds) of randomly selected bears that were anesthetized and measured. Because it is much more difficult to weigh a bear than to measure its chest size, the presence of a correlation could lead to a method for estimating weight based on chest size. Chest size (in) Weight (lb) (a) Construct a scatter diagram on the given axes (b) Calculate the linear correlation coefficient and write it below. Round your answer to two decimal places. Weight (lb) (c) Based on the linear correlation coefficient and your scatter diagram, would you say it is a good idea to use a regression line to estimate a bear's weight using its chest size? Please explain Chest size (in) (d) Find the equation of the regression line with chest size as the independent variable and the weight as the dependent variable, and write it below. Round any numbers in your equation to two decimal places. (e) Draw the regression line on the scatter diagram. Show your work for the two points you used to graph the line. (e) Interpret the slope of the regression line. Explain in words what the slope tells us about the relationship between the chest size and weight of a bear. Be specific.