MGMT 650 Fall 2016 Problem Set 21. Compute these probabilities: a. The probability of rolling the number 6 using one die. b. The probability of rolling the number 6 twice in 2 rollsusing only one die. c. If the probability of seeing a male house finch at abirdfeeder is . 45 and the probability of seeing afemale house finch is . 35, what is the probability ofseeing, first a male house finch, then a female housefinch, and finally another male house finch?d. There are only 2 type of Pokemon: rare and common. If the probability of finding a rare Pokemon at aPokestop is . 05, what is the probability that the first 8Pokemon that you find are common, and then youfind one rare Pokemon at a Pokestop that has a lureattached to it. Assume that you will find at least 9Pokemon in the 30 minutes that the lure is attached. 2. The following contingency table shows opinionabout global warming (nonissue vs. serious concern)among registered voters, broken down by political partyaffiliation (Democratic, Republican, and Independent. PartyOpinion on GlobalWarningNoniss Serious Totueconcern alDemocra50tic604400Republica50n2902100Independ20ent901100Total4407601200a)What is the probability that a randomly selectedregistered voter who is republican believes that globalwarming is a serious issue?b)What is the probability that a randomly selectedregistered voter is a republican given that he or shebelieves global warming is a serious issue?c)What is P (Serious Concern | Democratic) ?d)What is the probability that a registered voterselected at random believes that global warming is aserious issue?e)What is the probability that a registered voterchosen at random is a Republican and believes thatglobal warming is a serious issue?3. A company has recently replaced their e-mail serverbecause previously mail was interrupted on about 15% ofworkdays. To see how bad the situation was, calculate heprobability that during a 5-day work week, there would be ane-mail interruption: a) On Monday and again on Tuesday. b) For the first time on Thursday. c) Every day. d) At least once during the week. 4. A European department store is developing a newadvertising campaign for their new US location, and theirmarketing managers need to better understand their targetmarket. Based on survey responses, a joint probability tablethat an adult shops at their new US store identified by theirage is shown below: ShopYesNoTotalless 20 0. 26 0. 04 0. 30Age20-400. 240. 10. 34greater400. 12 0. 24 0. 36Total0. 620. 381. 00a)What is the probability that a survey respondent willshop at the US store?b)What is the probability that a survey respondent willshop at the store given they are younger than 20 years old. c)What is the probability that a survey respondent who isolder than 40 shops at the store?d)What is the probability that a survey respondent isyounger than 20 or will shop at the store?5. Look up resources for the “binomial probabilitydistribution”. Describe briefly what it is and give oneapplication for how it can be used. Use the distribution tofind the probability that one would get 16 heads in 20 tossesof a fair coin. Is this a small or large probability and why?6. A day trader buys an option on a stock that will return$100 profit if the stock goes up today and lose $400 if itgoes down. If the trader thinks there is a 75% chance thatthe stock will go up,a) What is the expected value of the option’s profit?b) What do you think of the option?7. According to Investment Digest (",Diversification andthe Risk/Reward Relationship",, Winter 1994, 1-3), the meanof the annual return for common stocks from 1926 to 1992was 15. 4%, and the standard deviation of the annual returnwas 21. 5%. During the same 67-year time span, the meanof the annual return for long-term government bonds was5. 5%, and the standard deviation was 7. 0%. The articleclaims that the distributions of annual returns for bothcommon stocks and long-term government bonds are bellshaped and approximately symmetric. Assume that thesedistributions are distributed as normal random variables withthe means and standard deviations given previously. Here is a link to the z table: http: //www. statsoft. com/textbook/sttable. htmla. What is the probability that the stock returns aregreater than 0%?b. What is the probability that the stock returns are lessthan 20%?8. A set of final examination grades in an introductorystatistics course is normally distributed with a mean of 73and a standard deviation of 8. a) What is the probability of getting a grade below 91 onthis exam?b) What is the probability that a student scored between65 and 89?c) The probability is 5% that a student scores higher thanwhat grade?d) If the professor grades on a curve (i. e. gives A’s to thetop 10% of the class, regardless of the score), are youbetter off with a grade of 81 on this exam or a grade of68 on a different exam, where the mean is 62 and thestandard deviation is 3? Why?