hey guys.
so long story short, i bit off more than i could chew with the take-home part of my specialist SAC and i have to solve
192600pi+60000=1254pi(x)+12500sin(pi(x)/100)-40000sin(pi(x)/200)
any help solving this would be greatly appreciated. Basically I'm looking for solutions of something in the form of a=bx+csin(dx)-esin(fx)
You already have something of that form.
Hey, I need some help
I was wondering where you might get the z 'value' for the confidence intervals. Like for the approximate 95% confidence interval, the z value is 1.96. I was wondering how you might get the z value for a 90% interval or an 85% interval etc.
Apparently we use the inverse normal function on our CAS, but I can't seem to recall it correctly...
Yup, you do. What you've gotta do is remember WHERE the z-value comes from - and from that, what even the hell a confidence interval is in the first place.
The easiest thought is that it's the interval in which you are "x% confident the true mean is". More strictly speaking, it's the interval over which there's a x% probability that the mean exists. Using notation (where Z is the standard normal distribution), for the 0.95 case this becomes:
Using our knowledge of normal distributions, we can rewrite this like so:
And now we'll use the fact that the sum of all probabilities is 1:
And now, the symmetry of the normal distribution:
Now, we simplify:
Which you can use the inverse normal calculator for! Try it out, you should get 1.96. To get this to work for some other percentage, just follow the same steps, let me know if you have any issues.
EDIT: TeX works differently to how I remember. D: Give me a bit to fix it up...
EDIT 2: Fixed!