Please help solve without using the excel function:

For 6 and 8: A standardized test was given to a set of high school juniors and the distribution of the data is bell shaped. The mean score is 800 and the standard deviation is 120.

6. To qualify for a special summer camp for accelerated students, a student must score within the top 16% of all scores on the test. What score must a student make to qualify for summer camp?

800+360=1160

1160

8. A student scores 900 on the test. How many more points did the student need to qualify for summer camp?

1160-9000

260

Please solve and explain how you arrive at 360 to add to the mean.

For 9,10, and 12: On the average, members at a local fitness center work out for 90 minutes with a standard deviation of 15 minutes. The distribution is normal.

9. What percentage of the fitness club members work out for 45 minutes or less? (Hint: This is only asking for 45 minutes or less.)

10. What percentage of the fitness club members work out for 2 hours and 15 minutes or more? (Hint: What value do I need to divide by 15?)

12. We can say that 99.85% of the fitness club members work out for no more than ____________ minutes. (Hint: Start by considering the number of standard deviations you need.)