Question

The mean yearly rainfall in Sydney, Australia, is about 134 mm and the standard deviation is about 66 mm ("Annual maximums of," 2013). Assume rainfall is normally distributed. How many yearly mm of rainfall would there be in the top 15%? Round answer to 2 decimal places. Answer:

Answer 1

Solution :

Given that,  

mean = = 134 mm

standard deviation = = 66 mm

Using standard normal table ,

P(Z > z) = 15%

1 - P(Z < z) = 0.15

P(Z < z) = 1 - 0.15

P(Z < 1.04) = 0.85

z = 1.04

Using z-score formula,

x = z * +

x = 1.04 * 66 + 134 = 202.64

yearly 202.64 mm of rainfall would there be in the top 15%