95% of students at school weigh between 62 kg and 90 kg. Assuming this data is normally distributed, what are the mean and standard deviation?
In a bell curve (normal distribution) 1 standard deviation + or - from the mean covers 34% (each direction for a total of 68%) . The second standard deviation covers 13.5% (each direction from the mean for 27%)
The MEAN will be exactly between 90 and 62 = 76 (the peak of the bell curve)
95% (34 + 34 + 13.5 +13.5) covers 2 positive and 2 negative standard deviations or FOUR standard deviations. 90-62 = 28 Each Standard deviation would be 28/4 = 7
Sorry, this is clearer with a picture which I cannot post here, but here is a link: (I think)
http://www.google.com/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&ved=0CAcQjRw&url=http%3A%2F%2Fnationalpainreport.com%2Fliving-well-bell-curve-8821914.html&ei=tdmZVc7EPMXOsAWpnZP4DQ&bvm=bv.96952980,d.aWw&psig=AFQjCNHhdNu6pdDh8HBtaf9XHiVCqvpBvQ&ust=1436232474284197
In a bell curve (normal distribution) 1 standard deviation + or - from the mean covers 34% (each direction for a total of 68%) . The second standard deviation covers 13.5% (each direction from the mean for 27%)
The MEAN will be exactly between 90 and 62 = 76 (the peak of the bell curve)
95% (34 + 34 + 13.5 +13.5) covers 2 positive and 2 negative standard deviations or FOUR standard deviations. 90-62 = 28 Each Standard deviation would be 28/4 = 7
Sorry, this is clearer with a picture which I cannot post here, but here is a link: (I think)
http://www.google.com/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&ved=0CAcQjRw&url=http%3A%2F%2Fnationalpainreport.com%2Fliving-well-bell-curve-8821914.html&ei=tdmZVc7EPMXOsAWpnZP4DQ&bvm=bv.96952980,d.aWw&psig=AFQjCNHhdNu6pdDh8HBtaf9XHiVCqvpBvQ&ust=1436232474284197
