broodjepanda Posted January 10, 2017 Share Posted January 10, 2017 I have two questions for my homework, it would be very nice if someone can help me with this.Question 1: Exam candidates for the driving test have success rate of 60%, how likely is it that 60 students or more pass from the 100 students. Question 2: a machine fills the bottles with cola, it is distributed normally with an average of u = 300 ml and a standard deviation of 3mlHow likely is it that a Random bottle contains less than 299 milliliters, give an explanationHow likely is it that the average content of any 6 bottles is less than 299ml? Please specify Sorry for the bad english Quote Link to comment Share on other sites More sharing options...
Aiban Posted January 10, 2017 Share Posted January 10, 2017 Dis made chatbox lit fam come 3 Quote Link to comment Share on other sites More sharing options...
Solution Posted January 10, 2017 Share Posted January 10, 2017 I have two questions for my homework, it would be very nice if someone can help me with this. Question 1: Exam candidates for the driving test have success rate of 60%, how likely is it that 60 students or more pass from the 100 students. Question 2: a machine fills the bottles with cola, it is distributed normally with an average of u = 300 ml and a standard deviation of 3ml How likely is it that a Random bottle contains less than 299 milliliters, give an explanation How likely is it that the average content of any 6 bottles is less than 299ml? Please specify Sorry for the bad english Question 1: 100% statistically 60% should pass, which means it's 100% LIKELY that 60 will pass. Question 2: with a standard deviation of 3 it'll most likely be between -3 and +3 deviation from 300ml. With 6 bottles you ought to end up with -1, +1, -2, +2, -3, +3 2 of them will end up being lower than 299 (298 and 297ml) your chances of hitting one of these 2 bottles when going through them is 2/6 = 1/3. so 33.33% riiiiiiight? Quote Link to comment Share on other sites More sharing options...
Team Cape Posted January 10, 2017 Share Posted January 10, 2017 (edited) 1. I assumed the first one was binomial, so i used binomcdf(100, 0.6, 60) on my caluclator and got a 53.79% chance. Not totally sure on this one, but this is what I got. 2. It's given that it's normal, so use normalcdf(-infinity, 299, 300, 3) (or you could use a table but thats very tedious). Comes out to 36.944% - This means that 36.944% of bottles will contain less than 299mL. This one is definitely right. 3. I multiplied the distribution by 6 (so it would be ~ Nor(1800, 18)), and I decided to look for 1794. I believe this should be the same probability (someone can correct me if I'm wrong). I plugged in normalcdf(-infinity, 1794, 1800, 18), and I got 36.944% Edit: I did all this in AP Stats like a couple months ago, so my memory is hazy. This is what I got though. I don't think #3 is right. Edited January 10, 2017 by Imateamcape 1 Quote Link to comment Share on other sites More sharing options...
broodjepanda Posted January 10, 2017 Author Share Posted January 10, 2017 1. I assumed the first one was binomial, so i used binomcdf(100, 0.6, 60) on my caluclator and got a 53.79% chance. Not totally sure on this one, but this is what I got. 2. It's given that it's normal, so use normalcdf(-infinity, 299, 300, 3) (or you could use a table but thats very tedious). Comes out to 36.944% - This means that 36.944% of bottles will contain less than 299mL. This one is definitely right. 3. I multiplied the distribution by 6 (so it would be ~ Nor(1800, 18)), and I decided to look for 1794. I believe this should be the same probability (someone can correct me if I'm wrong). I plugged in normalcdf(-infinity, 1794, 1800, 18), and I got 36.944% Edit: I did all this in AP Stats like a couple months ago, so my memory is hazy. This is what I got though. I don't think #3 is right. Well you got me in the right direction, thanks! 1 Quote Link to comment Share on other sites More sharing options...
Solution Posted January 10, 2017 Share Posted January 10, 2017 1. I assumed the first one was binomial, so i used binomcdf(100, 0.6, 60) on my caluclator and got a 53.79% chance. Not totally sure on this one, but this is what I got. 2. It's given that it's normal, so use normalcdf(-infinity, 299, 300, 3) (or you could use a table but thats very tedious). Comes out to 36.944% - This means that 36.944% of bottles will contain less than 299mL. This one is definitely right. 3. I multiplied the distribution by 6 (so it would be ~ Nor(1800, 18)), and I decided to look for 1794. I believe this should be the same probability (someone can correct me if I'm wrong). I plugged in normalcdf(-infinity, 1794, 1800, 18), and I got 36.944% Edit: I did all this in AP Stats like a couple months ago, so my memory is hazy. This is what I got though. I don't think #3 is right. Wew dis makes more sense 2 Quote Link to comment Share on other sites More sharing options...
Team Cape Posted January 10, 2017 Share Posted January 10, 2017 Well you got me in the right direction, thanks! Ahhh here we go. For #3: u is an unbiased estimator so we can assume the mean is the same. Since the parent distribution is x also normal, we also know that it's normal. This should follow the 10% rule as well. So the distribution we use is ~ Nor(300, 3/sqrt(6)) which is ~ Nor(300, 1.225). So now we can plug this into the calculator. normalcdf(-infinity, 299, 300, 1.225) = 20.711% chance. I'm fairly sure this is correct. Quote Link to comment Share on other sites More sharing options...
ez11 Posted January 10, 2017 Share Posted January 10, 2017 Question 1: 100% statistically 60% should pass, which means it's 100% LIKELY that 60 will pass. Question 2: with a standard deviation of 3 it'll most likely be between -3 and +3 deviation from 300ml. With 6 bottles you ought to end up with -1, +1, -2, +2, -3, +3 2 of them will end up being lower than 299 (298 and 297ml) your chances of hitting one of these 2 bottles when going through them is 2/6 = 1/3. so 33.33% riiiiiiight? that wasnt a very good @Solution 1 Quote Link to comment Share on other sites More sharing options...
Solution Posted January 10, 2017 Share Posted January 10, 2017 that wasnt a very good @Solution 2shit at statistics lul this is why I went with trigonometry n shit, much easier Quote Link to comment Share on other sites More sharing options...
Team Cape Posted January 10, 2017 Share Posted January 10, 2017 2shit at statistics lul this is why I went with trigonometry n shit, much easier :P Quote Link to comment Share on other sites More sharing options...
