Question

The life time of a certain kind of batteries has a mean life of 400 hours and standard deviation as 45 hours. Assuming the distribution of life to be normal, find i) the percentage of batteries with a life time of atleast 470 hours. Ii) Out of 10000 batteries how many batteries do you expect to have life between 385 and 415 hours.

Answer 1

This page will replace any tables or charts in the back of texts or handouts you might have been given

http://davidmlane.com/hyperstat/z_table.html

enter:
mean -- 400
SD -- 45
click on "above" and enter 470
prob is .0599 ---> 5.99%

ii) click on "between" and enter the values
multiply the prob by 10000

The beauty of this page is that you don't have to find z-scores first.
If your course requires you to work with z-scores, then find those scores for all your numbers, and set the mean to 0 and the SD to 1, then enter the data as z-scores.
You will get the same results.