The yearly rainfall in Vancouver, B.C. follows a normal distribution with standard deviation 172 mm. In 20% of years, the city gets over 1200 mm of rain. What is the mean annual rainfall in Vancouver (in mm)?

Question

The answer is 1055.5 mm....not sure how to get this answer.

Answer 1

a z-score table will give the number of s.d. above the mean for the 20% figure

the z-score is .84

so 1200 mm is .84 s.d. above the mean

1200 - (.84 * 172) = ?

Answer 2

why is the z-score 0.84

Answer 3

took me way too long but i got it:

1 - .20 = .8000
*Did this because you are looking for P(x>1200) therefore, you are looking at for a right side probability, z table only give you left.

Find .8000 INSIDE z chart, the closest number is .7995 = .84

x - (z*std.dev) = 1200 - (.84*172) = 1055.5