6.7 Use your calculator to simulate a couple's having children until they have a girl or until they have four children, whichever comes first.
The data are independent.
I set 1 equal to a boy and 2 equal to a girl. I then used randInt(1,2,40) and got the answers (2 2 1 2) So the first child they would have is a girl. From 6.6 their second child was a girl.
6.7) Question 6.7 asks you to use a calculator to simulate a couple's having children until they have a girl or until they have four children. I did ten random number samples on my calculator. I set it up like this: randint(1,2,4), 1=girls 2=boys. I did this ten times and here are my results: 2211 2112 1111 1122 1111 2111 2222 2222 2122 1212 The probability that I obtain for having a girl for the couple is 80%. The result for Example 6.6 was 93% so my results are a little bit lower than theirs.
6.19) Shaq makes about half of his free throws. Do a simulation with 100 free throws where 50% of his shots are made. 1=hit, 0=miss. a) (0,1,100) b) Shaq makes about 51% of his shots. c) The longest sequence of shots made was 7. The longest sequence of shots missed was 6. The variables are independent.
6.19 a) It is predicted that B-Ball player Shaqiulle O'neal makes about 50% of his free throws. We are to make a simulation of 100 free throw shots to see if this is true. b) All of Shaq's free throw shots are independent of each other because he is shooting a new shot each time. c) In this prob., I assigned a 0 to his made shots and a 1 to his missed shots. In the end, through 100 attempts, I calculated that Shaq will make 52 free throws and miss 48 free throws, for a percentage of 52%. The longest streak of made shots was 6; the longest streak of miss shots was 7.
A)Any baseball team in the National League has as a 60% chance of winning any game in the World Series. To win the World Series a team must win 4-7 games. The variables are independent because a team must win or lose, the game can't end in a tie. The results said that a team won 5 games out of 7 (2 loss). B) Another factor could be a team having a bad day, the weather, or injuries.
6.7- Use yoiur calculator to sumulate a couple's having children until they have a firl or until they have four children, whichever comes first.
The data are independent.
I set 1 equal to a boy and 2 equal to a girl. I used the calculator to get my answers. I used Randint(1,2,4) and got the set 1 2 2 1. Their second child would be a girl and they have a 50% chance of having a girl.
In 6.6, their third child was a girl.
Mrs. Hankes, my e-mail address is kelsy.reisinger@gmail.com
Professional tennis players carry multiple rackets to each game. A coach said that the tennis player has a 15% chance of breaking the racket. The variables are independent because the tennis plater either has a usable racket, or they don't. It would take 22 matches until a tennis player would have to use a back up racket.
6.16) A baseball player has a batting average of .320. Batting average= (#of hits)/(# of at-bats). a)(0,1,20) 0=misses, 1=hits b)repeat 20 times. c) After my simulation, his batting average would be above .320. The data are independent.
6.10- Simulating Families: In this question there are a large group of families with four children each. Estimate the percent of families that have exactly 0 girls, 1 girl, 2 girls, 3 girls, and 4 girls. The data is independent.
Assign numbers: 1 and 2 are girls and 3 and 4 are boys, do random digits between 1 and 4 and 4 numbers at a time since each family has 4 kids.
Percent of families that have exactly: 0 girls- 10% 1 girl- 10% 2 girls- 47.5% 3 girls- 27.5% 4 girls- 5%
6.8- Suppose that in a particular year the Americal League baseball team is considered to have a 60% chance of beating the National league team in any given World Series game. (This assumption ignores any possible home field advantage, which is probably not very realistic.) To win the World Series, a team must win 4 out of 7 games in the series. Further assume that the outcome of each game is not influenced by the outcome of any other game (that is, who wins one game is independent of who wins any other game). a)Use simulation methods to approximate the number of games that would have to be played in order to determine the world champion. b)The so-called home field advantage is one factor that might be an explanatory variable in determining the winnder of a game. What are some other possible factors?
The data are independent.
I used Randint(1,10,7) on my calculator. I set 1-6 equal to win and 7-10 equal to a loss. I came up with (1 8 4 7 9 10 6)
Wins-3 Losses-5
a)6 games would have to be played to determine the world champion, since the team lost thair fourth game on game number 6. The 7th game is not necessary. b)Practice intensity in the days approaching the game could make one tired or not. Personal issues can also determine how a player plays that day.
6.10-There are a large group of families, all with 4 children. Use a simulation to estimate what percent of the families have 0 girls, 1 girl, 2 girls, 3 girls, and 4 girls. A. Describe a correspondence between random digits and outcomes one could use to perform the simulation. -You could set up a random integer on your calculator, using 0 as your minimum and 4 as your maximum. 0 would stand for 0 girls, 1 could stand for 1 girl, 2 for 2 girls, 3 for 3 girls, and 4 for 4 girls. B. Conduct 40 repetitions of the simulation, and calculate the percents specified above. - I use the min of 0, max of 4, and 40 as the number of repitions. The proportions I got were as follows: 0 girls- .075 or 7.5% 1 girl- .25 or 25% 2 girls- .175 or 17.5% 3 girls- .25 or 25% 4 girls- .25 or 25%
6.9- A tennis player's coach tells him that his raquet has a 15% chance of breaking in any given match. How many matches can he play before his raquet breaks? - I set up a random integer on my calculator, using 0 as my min, 99 as my max, and 100 as my repetitions. 0-14 means his raquet breaks and 15-99 means it works. The first time any number 0-14, his raquest breaks. My data is a follows: 1. Broke game 6. 2. Broke game 22 3. Broke game 3. 4. Broke on game 9. 5. Broke on game 9.
On average, the players raquet broke every 9.8 games.
6.10 a) In this problem, a family is having 4 children; they want to know, through a series of 40 repititions, what the chance is of them having 0 girls, 1 girl, 2 girls, 3 girls, and 4 girls. b) The variable girls is independent because each time they have a child, the next child's sex will not be affected. c) In my simulation, I assigned: 0 girls = 0 1 girl = 1 2 girls = 2 3 girls = 3 4 girls = 4 I then did 40 simulations of this experiment. These are my results: 0 girls = 22.5% 1 girl = 17.5% 2 girls = 17.5% 3 girls = 17.5% 4 girls = 25.0%
6.12 For a multiple choice test, you get 4 points for each question right and -1 for each wrong. There are 10 questions. Should you guess or leave it blank?
The data are independent.
There are 4 choices per question. There is a 25% chance. Then you will get 2.5 right. Guess instead of leave it blank because a blank paper has a score of zero.
6.11- The airport van: Each van carries 7 passengers. 25% of the time a passenger will fail to show up. If you allow 9 reservations for each van, what is the probability that more than 7 passengers will appear? The data is independent.
25% - no show 75% - show
0-24 No show 25-99 show
77.7% of the time 7 or less passengers will appear this means 22.3% of the time more than 7 passengers show.
6.19 Simulate Shaq's foul shooting of 100 shots. He is a 50 percent foul shooter. The data is indepentent misses-0 makes-1 my results were Shaq makes about 47percent of his foul shots. His most makes in a row were 7 and most misses in a row were 6.
6.16 Simualte a baseball players batting average for 20 at bats. His currant batting average is .320. Then repeat the simulation for 20 series of 20 at bats. The data is indepentent. -I assigned numbers 0-31 for hits and 32-99 as getting out. -After repeating 20 times i got the final batting average of this guy to be about .313. which is pretty close to the .320 batting average of the baseball player.
Question 6.10 asks for you to determine the likeliness that a family would have 0,1,2,3,or 4 girls out of 4 children. The question asked you to do the simulation 40 times. I let 1=girls and 2=boys. The percentages that I got were... 0 Girls = 7.5% 1 Girl = 15% 2 Girls = 37.5% 3 Girls = 32.5% 4 Girls = 7.5% The data are independent.
17 comments:
6.7 Use your calculator to simulate a couple's having children until they have a girl or until they have four children, whichever comes first.
The data are independent.
I set 1 equal to a boy and 2 equal to a girl. I then used randInt(1,2,40) and got the answers
(2 2 1 2)
So the first child they would have is a girl. From 6.6 their second child was a girl.
6.7) Question 6.7 asks you to use a calculator to simulate a couple's having children until they have a girl or until they have four children. I did ten random number samples on my calculator. I set it up like this: randint(1,2,4), 1=girls 2=boys.
I did this ten times and here are my results:
2211
2112
1111
1122
1111
2111
2222
2222
2122
1212
The probability that I obtain for having a girl for the couple is 80%. The result for Example 6.6 was 93% so my results are a little bit lower than theirs.
6.19) Shaq makes about half of his free throws. Do a simulation with 100 free throws where 50% of his shots are made. 1=hit, 0=miss.
a) (0,1,100)
b) Shaq makes about 51% of his shots.
c) The longest sequence of shots made was 7. The longest sequence of shots missed was 6.
The variables are independent.
6.19
a) It is predicted that B-Ball player Shaqiulle O'neal makes about 50% of his free throws. We are to make a simulation of 100 free throw shots to see if this is true.
b) All of Shaq's free throw shots are independent of each other because he is shooting a new shot each time.
c) In this prob., I assigned a 0 to his made shots and a 1 to his missed shots. In the end, through 100 attempts, I calculated that Shaq will make 52 free throws and miss 48 free throws, for a percentage of 52%. The longest streak of made shots was 6; the longest streak of miss shots was 7.
6.8-
A)Any baseball team in the National League has as a 60% chance of winning any game in the World Series. To win the World Series a team must win 4-7 games. The variables are independent because a team must win or lose, the game can't end in a tie. The results said that a team won 5 games out of 7 (2 loss).
B) Another factor could be a team having a bad day, the weather, or injuries.
6.7- Use yoiur calculator to sumulate a couple's having children until they have a firl or until they have four children, whichever comes first.
The data are independent.
I set 1 equal to a boy and 2 equal to a girl. I used the calculator to get my answers. I used Randint(1,2,4) and got the set 1 2 2 1. Their second child would be a girl and they have a 50% chance of having a girl.
In 6.6, their third child was a girl.
Mrs. Hankes, my e-mail address is kelsy.reisinger@gmail.com
6.9:
Professional tennis players carry multiple rackets to each game. A coach said that the tennis player has a 15% chance of breaking the racket. The variables are independent because the tennis plater either has a usable racket, or they don't. It would take 22 matches until a tennis player would have to use a back up racket.
6.16) A baseball player has a batting average of .320. Batting average= (#of hits)/(# of at-bats).
a)(0,1,20) 0=misses, 1=hits
b)repeat 20 times.
c) After my simulation, his batting average would be above .320.
The data are independent.
6.10- Simulating Families:
In this question there are a large group of families with four children each. Estimate the percent of families that have exactly 0 girls, 1 girl, 2 girls, 3 girls, and 4 girls.
The data is independent.
Assign numbers: 1 and 2 are girls and 3 and 4 are boys, do random digits between 1 and 4 and 4 numbers at a time since each family has 4 kids.
Percent of families that have exactly:
0 girls- 10%
1 girl- 10%
2 girls- 47.5%
3 girls- 27.5%
4 girls- 5%
6.8- Suppose that in a particular year the Americal League baseball team is considered to have a 60% chance of beating the National league team in any given World Series game. (This assumption ignores any possible home field advantage, which is probably not very realistic.) To win the World Series, a team must win 4 out of 7 games in the series. Further assume that the outcome of each game is not influenced by the outcome of any other game (that is, who wins one game is independent of who wins any other game).
a)Use simulation methods to approximate the number of games that would have to be played in order to determine the world champion.
b)The so-called home field advantage is one factor that might be an explanatory variable in determining the winnder of a game. What are some other possible factors?
The data are independent.
I used Randint(1,10,7) on my calculator. I set 1-6 equal to win and 7-10 equal to a loss.
I came up with (1 8 4 7 9 10 6)
Wins-3 Losses-5
a)6 games would have to be played to determine the world champion, since the team lost thair fourth game on game number 6. The 7th game is not necessary.
b)Practice intensity in the days approaching the game could make one tired or not. Personal issues can also determine how a player plays that day.
6.10-There are a large group of families, all with 4 children. Use a simulation to estimate what percent of the families have 0 girls, 1 girl, 2 girls, 3 girls, and 4 girls.
A. Describe a correspondence between random digits and outcomes one could use to perform the simulation.
-You could set up a random integer on your calculator, using 0 as your minimum and 4 as your maximum. 0 would stand for 0 girls, 1 could stand for 1 girl, 2 for 2 girls, 3 for 3 girls, and 4 for 4 girls.
B. Conduct 40 repetitions of the simulation, and calculate the percents specified above.
- I use the min of 0, max of 4, and 40 as the number of repitions. The proportions I got were as follows:
0 girls- .075 or 7.5%
1 girl- .25 or 25%
2 girls- .175 or 17.5%
3 girls- .25 or 25%
4 girls- .25 or 25%
6.9- A tennis player's coach tells him that his raquet has a 15% chance of breaking in any given match. How many matches can he play before his raquet breaks?
- I set up a random integer on my calculator, using 0 as my min, 99 as my max, and 100 as my repetitions. 0-14 means his raquet breaks and 15-99 means it works. The first time any number 0-14, his raquest breaks. My data is a follows:
1. Broke game 6.
2. Broke game 22
3. Broke game 3.
4. Broke on game 9.
5. Broke on game 9.
On average, the players raquet broke every 9.8 games.
6.10
a) In this problem, a family is having 4 children; they want to know, through a series of 40 repititions, what the chance is of them having 0 girls, 1 girl, 2 girls, 3 girls, and 4 girls.
b) The variable girls is independent because each time they have a child, the next child's sex will not be affected.
c) In my simulation, I assigned:
0 girls = 0
1 girl = 1
2 girls = 2
3 girls = 3
4 girls = 4
I then did 40 simulations of this experiment. These are my results:
0 girls = 22.5%
1 girl = 17.5%
2 girls = 17.5%
3 girls = 17.5%
4 girls = 25.0%
6.12 For a multiple choice test, you get 4 points for each question right and -1 for each wrong. There are 10 questions. Should you guess or leave it blank?
The data are independent.
There are 4 choices per question. There is a 25% chance.
Then you will get 2.5 right.
Guess instead of leave it blank because a blank paper has a score of zero.
6.11- The airport van:
Each van carries 7 passengers. 25% of the time a passenger will fail to show up. If you allow 9 reservations for each van, what is the probability that more than 7 passengers will appear?
The data is independent.
25% - no show
75% - show
0-24 No show
25-99 show
77.7% of the time 7 or less passengers will appear this means 22.3% of the time more than 7 passengers show.
6.19 Simulate Shaq's foul shooting of 100 shots. He is a 50 percent foul shooter. The data is indepentent
misses-0
makes-1
my results were Shaq makes about 47percent of his foul shots.
His most makes in a row were 7 and most misses in a row were 6.
6.16 Simualte a baseball players batting average for 20 at bats. His currant batting average is .320. Then repeat the simulation for 20 series of 20 at bats. The data is indepentent.
-I assigned numbers 0-31 for hits and 32-99 as getting out.
-After repeating 20 times i got the final batting average of this guy to be about .313. which is pretty close to the .320 batting average of the baseball player.
Question 6.10 asks for you to determine the likeliness that a family would have 0,1,2,3,or 4 girls out of 4 children. The question asked you to do the simulation 40 times. I let 1=girls and 2=boys. The percentages that I got were...
0 Girls = 7.5%
1 Girl = 15%
2 Girls = 37.5%
3 Girls = 32.5%
4 Girls = 7.5%
The data are independent.
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