How you answer a question like this depends on the type of technology you are expected to have access to. If you only have the Standard Normal Tables then you must change your distribution to the Standard Normal. This is easily done.
If X is a normal distribution, then (X-mean)/std dev is a Standard Normal.
Your mean = 500, std dev = 100, so (X-500)/100 is a Standard Normal distribution.
Z is a Standard Normal distribution (mean=0, std dev=1). This is what you look up if you are using the Standard Normal Tables
- P(450 < X < 700) = P((450-500)/100 < (X-500)/100 < (700-500)/100)
= P(-50/100 < (X-500)/100 < 200/100)
= P(Z<2) - P(Z<-.5) - arriving here from the previous line step might require some thinking :)
≅ .9772 - .3085 ≅ .6687
Most important is to understand that these probabilities can be thought of as areas under the normal curve (bell curve).
Check this graph on Desmos: https://www.desmos.com/calculator/rov1xwficz
You can change parameters: a = mean, b = standard deviation, c = lower bound, d= upper bound. Play around with changing these parameters. You can calculate any normal distribution probabilities with this.
Once you get a handle on these things, #2 and #3 will be good practice to check your understanding. Come back to us to check your work! Good luck!
