Statistics-You are charged with the responsibility to determine the probability of coincidental birthdays
Question;You are charged with the responsibility to determine the probability of coincidental birthdays. Initially the following two birthday questions were assigned to you.a. Ignoring leap years, find the probability that two randomly chosen people were born on January 1.b. Ignoring leap years, find the probability that two randomly selected people have the same birthday.c. You have a bag containing 1 red ball, 2 blue balls, 3 yellow balls, 4 black balls and 5 white balls. What is the probability of drawing without replacement a red ball, then a blue ball and lastly a yellow ball in the first three draws?d. For problem 3c how many different combinations are possible for the draw?e. For problem 3c how many different permutations are possible for the draw?f. A statistics professor tosses three coins that cannot be seen by any student. One student asks if at least one of the coins turned up heads and another student asks the same question for tails. Given that the professor?s response to both questions is ?yes?, find the probability that two of coins turned up heads?4. ROUNDED TO WHOLE NUMBER ANSWERS. Last semester in the undergraduate course I was teaching I decided that I would curve the course and, thus, I had to determine where the break in grades would occur. One hundred students were enrolled in the course and the points earned were normally distributed with a mean of 500 and a standard deviation of 50. Therefore, what would the point total be that would separate:a. A grade of F from D if the bottom 10% of the students was to receive a grade of F.b. A grade of B from C if the top 30% of the students was to receive a grade of A or B.5. FOUR DECIMAL ANSWERS. In the 113th Congress, the United States House of Representatives has 78 women representative with 59 being democrats and 19 being republicans. If a lobbyist for AARP randomly selects three different representatives to visit what is the probability that:a. All of the representatives would be women?b. Two of the representatives would be women?c. All would be women and republican provided the lobbyist was only going to select from the women representatives?6. You have just completed your dual MHR/IR degrees and are looking for a professional position during this time when entering salaries are negatively skewed. During your interview process three companies have offered you a position: 1) INTERALIA CORPORATION has offered you the mode entry salary, 2) PAYSMOST INCORPORATED has offered you the mean entry salary, and 3) ROCKYROAD COMPANY has offered you the median entry salary. Assuming all other things are equal, which offer should you accept? Justify your answer!7. TWO DECIMAL ANSWERS: Listed below are measured amounts of carbon monoxide (in ppm over an 8 hour period) in the air. EPA has established an average air quality standard for carbon monoxide as 9 ppm over an 8 hour period. The measurements were recorded in downtown Oklahoma City on extremely busy driving days in January 2014.a. Use the values below to construct a 95% confidence interval estimate of the mean amount of carbon monoxide in the air during all of January 2014.9.45 10.67 10.45 8.45 7.60 7.40 8.60 6.75b. Based on the confidence interval would you be concerned about the carbon monoxide levels in OKC? Why or why not?8. THREE DECIMAL ANSWERS: Determine the mode, the median and the variance for the SAMPLE DATA in Problem #7.9. FOUR DECIMAL ANSWERS: The Zero Mutual Fund Company has an Insider Trading Mutual Fund that is supposed to sell for $10 a share. When the selling prices per share on 1000 transactions were randomly selected, they revealed that the mean selling price was $10 with a standard deviation of $1. Assuming a symmetrical distribution for the selling price per share, solve the following problems:a. What percent of the shares sold for $12 or more?b. What percent of the shares sold for $8 or less?c. What percent of the shares sold between $9 and $11?d. What percent of the shares sold for $8 to $9?10. What is the BEST research method to determine the following: (just list the method and nothing else!!!!)a. If Lily?s new Alzheimer pill is helpful in preventing Alzheimer?b. How first responders and hospitals would respond to a terrorist attack on downtown Oklahoma City?c. The differences in the attitudes of truants and a matched sample of non-truants.d. Who shoplifts at Walmart?11. PART ROUNDED TO WHOLE NUMBER AND THE REST TWO TO FOUR SIGNIFICANT DIGITS: A national scholarship program requires applicants to take an IQ test to determine eligibility for the scholarship. IQ scores are normally distributed with a? of 100 and a?? of 10. Using these data answer the following questions.a. If a college admission office requires scores of at least the 60th percentile for admission, what is the cutoff score?b. What is the probability of randomly selecting a ?test taker? with a score1) Greater than or equal 100?2) Less than or equal 75?3) Between 90 and 110?12. ANSWER IN % WITH TWO DECIMALS: Will the Volt be successful or go the way of the Oldsmobile and the Pontiac? That is the question the CEOs wants you to evaluate before GM commits funds to design the next generation of Volt and then to increase its production. Therefore, you randomly select 875 car owners looking to buy compact and mid-size GM cars and ask them if they are considering the purchase of a Volt. The results of your survey is 120 of these potential car buyers would consider buying a Volt?a. Find the 99% confidence interval for the true percentage of all compact and mid-size GM car buyers that would consider buying a volt?b. When you meet with the CEO after analyzing the answer, what is your answer to the question if GM wants 20% of these potential GM car buyers to consider the purchase of a Volt before the commitment of funds necessary for the program listed in the body of this problem?13. What are the average miles per gallon (mpg) for all new cars? Using Consumer Reports, a random sample of 35 new cars yielded an average of 21.1 mpg.a. Identify the variable.b. Is the variable quantitative or qualitative?c. What is the implied population14. A data set with whole numbers has a low value of 20 and a high value of 119. Find the class width (interval width) and the class limits for a frequency distribution with 5 classes.15. The Sky Ski team has five entrants in a women?s slalom event. The coach would like the first, second and third places to go to SS members. In how many ways can the five team entrants achieve the coach?s goal?
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