HELP ASAP THANKS

Question

The results of an examination are found to be normally distributed with a standard deviation of 15.0. If a student is selected at random, the probability is 0.0485 that his mark will exceed 85. The mean for this test correct to the nearest tenth is?

Answer 1

Obtain a z-table: http://www.stat.ufl.edu/~athienit/Tables/Ztable.pdf

Probability of exceeding 85 at 0.0485, places the results at 0.9995.

0.9995 has a z-score of 3.27 to 3.32

3.27 ≤ (85 - μ) / 15 ≤ 3.32

49.05 ≤ 85 - μ ≤ 49.8

-35.95 ≤ -μ ≤ -35.2

35.95 ≥ μ and μ ≥ 35.2

35.2 ≤ μ ≤ 35.95