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Raul is interested in knowing if time is a factor that has to do with car accidents. He proposed to settle in the “Periferico” where most cars pass and move, with a cinemometer to detect the speed of the cars. He considered three hours, early, mid-afternoon, and night. He collected data to perform a statistical analysis with those 3 respective hours to reach a firm conclusion. What type of study is this example? Observational/Experimental?
Answer: Observational
It is the unbiased group that does not receive the experimental procedure, and that helps us know if there is a difference in the experiment.
Answer: Control group
Andrés is working at a summer camp, he is in charge of 12 kids during the mornings all the week. Every morning he prepares breakfast and gives a chocolate bar as a dessert to each child. What type of study is this example? Population/Sample?
Answer: Population
A true or false question, what type of measurement level is it?
Answer: Nominal (not natural order)
Having a savings account and saving $100 every week, what type of measurement level is it?
Answer: Ratio (it has a beginning point)
A bingo game has numbers from 1 to 80. Which is just about to start. So all numbers remain available. What is the probability that a number divisible by 8 or 5 will come up?
Answer: P(# divisible by 5 or 8) = 16/80+8/80 = 24/80= 3/10 (not mutually exclusive)
A teacher has 15 chocolates, 7 white, 4 dark, and 4 milk. What is the probability that you get 1 of white type and 2 of dark, after 3 attempts have already been produced, which have come up with 2 milk and one dark?; considering that after they take the chocolate in each attempt randomly, it is being consumed.
Answer: Dependent = P(come up 1 white and 2 of dark type, after 2 milk and one dark have come up without replacement)= 7/12*3/11*2/10 = .03
From a deck of 52 cards. What is the probability of getting a king and an odd number? Considering the ace as a number rather than a face card. Since there are many interpretations of it today that says that it is a face, but in this case not.
Answer: Independent = P (king and odd number) = 4/52 * 20/52 (including the 4 aces) = .030
From a deck of 52 cards. What is the probability of getting a king or a queen?
Answer: Mutually exclusive = P(king or queen) = 4/52 + 4/52 = 8/52 = 2/13
You have in a bag 10 marbles, 5 red, 2 green, and 3 blue. What is the probability that you choose one red and one blue, if it is being replaced when each attempt is being produced?
Answer: Independent = P( choosing red and blue) = 5/10 * 3/10 = .15
In my NFL fantasy team, I must choose 3 running backs from a roster of 18 running backs. How many different ways can I choose the running backs?
Answer: Combination = 18C3 = 816 ways
In how many ways can a group of 12 dads sit up in the classroom to hear and watch Ms. Quiroz open house?
Answer: Factorial = 12! = 479,001,600 ways
If Renata has 6 shirts, 7 skirts, 9 pairs of socks, 15 glasses, 6 bracelets, and 4 pairs of shoes. How many outfits can she make?
Answer: Multiplication rule = 6*7*9*15*6*4= 136, 080 outfits she can make
In how many ways can 7 of a group of 17 teachers be seated in the auditorium to witness the graduation ceremony of the seniors “Class 2021”?
Answer: Permutation = 17P7 = in 98,017,920 ways
You have been given by an Adidas designer a list of 130 pairs of shoes designs. You are assigned to create your top 3 favourite pairs of shoes from that list, so they can go on the market. In how many ways you can do it?
Answer: Permutation = 130P3 = 2,146,560 ways
Out of 15 soccer and 12 basketball players, a team consisting of 11 soccer players and 5 basketball players is to be formed. In how many ways can this be done if one particular basketball player must be in the team?
Answer: Combination = 15C11 * 11C4 = 450,450 ways
For an ASOMEX tournament, coach Gaitan must make a swimming group of 8 students randomly, from a list that contains 15 middle school students and 20 high school students. In how many ways can he create a group of 8 students with at least 5 of the students chosen being from highschool?
Answer: Combination = 20C5 * 15C3 = (7054320) + 20C6 * 15C2 = (4069800) + 20C7 * 15C1 = (1162800) + 20C8 = (124970)
*7054320 + 4069800 + 1162800 + 124970 = 12,411,890 ways
2) There is a swimming competition where there are 20 participants. The prices will be for the 1st, 2nd and 3rd places. What is the probability that Luisa, David, and Astrid won first, second, and third place respectively?
Answer: P (Luisa - 1st, David - 2nd, and Astrid - 3rd) = 20P3 = 1/6840
A president, vice president, secretary, and treasurer for the NHS organization are chosen from a list of 76 members that make up said organization. What is the probability that Gustavo, DIego, David, and Erick are chosen as president, vice president, secretary, and treasurer respectively?
Answer: P( Gustavo - president, Diego - vice president, David - secretary, and Erick - treasurer) = 76P4 = 30,791,400 = 1/30,791,400
3) A basketball team must be created. From a list of 10 participants, which includes 5 girls and 5 boys. A team of 5 integrants must be created. What is the probability that the coach makes a team made up of 3 boys and 2 girls?
Answer: P(3 girls and 2 boys) = 5C3 * 5C2 = 100 /10C5 = 252 = 100/252 = 25/63