Name: Langholz Fall 2012Midterm 2 Review1. Lupus is a medical phenomenon where antibodies that are supposed to attack foreign cells to preventinfections, see plasma proteins as foreign bod ie s, leadin g to a high risk of clotting. It is believed that 2%of the population suffer from this disease.The test for lupus is very accurate if the person actually has lupus, however is very inaccurate if theperson doe s not. More specifically, the test is 98% accurate if a person actually has the disease, meaningthat the probability of a positive test result when a person actually has lupus is 0.98. The test is 74%accurate if a person does not have the disease, meaning that the probability of a negative test result whena person does not actually have lupus is 0.74.Dr. Gregory House’s team presents him a case where the patient tested positive for lupus. However Dr.House claims that “It’s never lupus, ” even though the test result is positive. What do you think? (Hint:What is the probability that a person who t es t ed positive actually has lupus? )2. In a classroom with 24 students, 7 students are wearing jeans, 4 students are wearing shorts, 8 students arewearing skirts, and the rest are wearing leggings. If we randomly select 3 students without replacement,what is the probability that one of the selected students is wearing leggings and the other two are wearingjeans?Name: Langholz Fall 20123. 20% of students at a c oll e ge own a car, 35% own a bike and 5% own both a bike and a car.(a) Make a contingency table or a venn diagram summarizing this information.(b) What percent of students at this college own a car or a bike?(c) What percent of students at this college do not own a c ar or a bike?(d) What percent of students own a car but not a bike?(e) What percent of students own a bike but not a car ?(f) Are owning a car and a bi ke independent?4. Based on the figure below which of t h e foll owing statements is (are) true.(A) A and B are mutually exclusive (disjoint).(B) A and B are independent because they cannot happenat the same t i me.(C) P(A or B) = 0.43 * 0.27 = 0.1161(D) P(A and B) = 0.43 + 0. 27 - (0.43 * 0.27) = 0.5839(E) If A doesn’t happen B must happen.(F) A and B are d ependent.5. Answer the following questions.(a) If a fair coin is tossed many times and the last eight tosses are all heads, the n the chance thatthe next toss will be head s is somewhat less than 50%. True or false and justify.(b) A coi n is tossed and you win a prize if ther e are more than 60% heads. Would you be surprised i fthe c oin landed on heads more than 60% of the time in 10 tosses? in 100 tosses? Which is moresurprising? Which is better in order to win the prize: 10 tosses or 100 tosses? Explain.(c) A coin is tossed and you win a prize if there are more than 40% heads. Wh i ch is better : 10 tossesor 100 tos ses ? Explain.(d) A coin is tossed and you win a prize if th er e are between 40% and 60% heads. Which is better:10 t oss es or 100 tosses? Explain.4Name: Langholz Fall 20126. Determine if the below statements are true of false and explain your reasoning.(a) Drawing a face card (jack, qu een , or kin g) and drawing a red card from a full deck of playing car dsare mutually exclusive events(b) Drawing a face card and drawing an ace from a full de ck of playing cards are mutually exclusiveevents.7. For commercial flights in 2009, approximately 80% of flights arrived on time, according to the Bureau ofTransportation Statistics.(a) If you randomly select 3 flights and assume they are i n de pendent, what is the probability that twoor three will arrive on time?(b) What is the probability that at least one of the 3 flights will be late?(c) If you randomly select 150 flights and assume they are independent, what is the probability that 114or fewer arrive on time?8. Uncle Frank loves to fish. After years of fishing he has discovered the fish in the lake h e goes to havenormally distributed weight with a m ean of 20 oz. and a s tan d ard deviation of 6 oz. Uncle Frank getsreally excited if he catches one of the heaviest (top) 10% of fish in the lake. What is the cut off for theheaviest 10% of fish in t he lake?(a) 27.68(b) 12.32(c) 30.58(d) 24.389. Suppose that the proport i on of the adult population who jog is 0.15. Based on t h is information, whichof the following statements is (are) true?(A) If we were to take 60 random samples of 40 adults and plotted t h e proportion of joggers, theresulting distribution would be right skewed.(B) If we were to take 600 random samples of 40 adults and plotted the proportion of joggers, theresulting distribution would be symmetric.(C) A random sample of 80 adults where 22% ar e joggers would be considered unusual.(D) A random sample of 160 where 22% are jogger s would be considered unusual.(E) Increasing the sample size from 80 to 160 would cut the standard dev iat i on of the sample pro-portion in h al f.10. In the 2010 Midterm Election 35% of potential voters in California actually voted. (Note that thi s35% i s a rough estimate but we will take it as a given for the purpose of this question.)(a) Which of the following does not need to be satisfied in order to be able to use the Central LimitTheorem to describe the sample proportion of potential Californian voters who actually voted inthe 2010 M i d te r m Elect ion .(A) The sample needs to be random.(B) The sample size needs to be less t h an 10% of all potential Californian voters.(C) There should be at least 10 “s uc ce sse s” and 10 “failures” in the sample.(D) The sample size needs to be greater than or equal to 30.(b) Which of the below is true about the shape, center and spread of the distribution of the sampleproportion of potential Californian voters who actually voted in random samples of size 100.Make sure to check for the correct notat i on.(A) ˆp ∼ N�mean =0.35,SD =�0.35∗0.65100=0.0477�(B) ¯x ∼ N�mean =0.35,SD =�0.35∗0.65100=0.0477�(C) ˆp ∼ N�mean =0.35,SD =0.35√100=0.035�(D) ¯x ∼ N�mean =0.35,SD =0.35√100=0.035�(c) Calculate the probability t hat i n a random sam ple of 100 potential Californian voters majority(more than 50%) has voted.7Name: Langholz Fall 201211. A poll of 1,073 randomly selected adults found that 784 of the respondents wanted Congress to pass astimulus bill to rescue the economy.(a) Report a 95% confidence interval for the population proportion percentage in favor of a stimulus bill.(The conditions for using the CLT have