Are you aware of the 68, 95, 99.7 rule?
Hiya guys/girls. I have a self study stats assignment to do which I have completed apart from one question where I have no idea what to do. Any help would be amazing.
" a batch of 800 components produced by a machine is expected to be normally distributed. A sample was taken and measured and found to have a mean of 15mm with a standard deviation of 0.02. Calculate how many of the batch will have a length:
a) between 15.00mm and 15.06mm
b) between 14.99mm and 15.05mm
c) greater than 15.04mm
d) less than 14.94mm"
once again thanks in advance for any help/advice/solutions
hi again ive read up on the 68 95 99.7 rule and it helped me find the answer for a) c) and d) however for b) im struggling as the numbers all between the deviation parameter so to speak. there any advice how I can get round this
If you can't use the 68, 95, 99.7 rule, then you have to do a few things:
1) Draw a diagram of your normal distribution and shade in the area you are trying to find, i.e. between say and . We can represent this area as .
2) Standardise your normal distribution, so that you get the corresponding standard normal values (say and ) using . This means that you will be making use of the fact that
3) If you want to find then you need to realise that this is equal to . If you have a diagram, can you see why this is? These two values can be read from a standard normal distribution table, though you may have to apply some symmetry as well.