Question

The mean yearly rainfall in Sydney, Australia, is about 137 mm and the standard deviation is about 69 mm ("Annual maximums of," 2013). Assume rainfall is normally distributed.

a.) State the random variable.

b.) Find the probability that the yearly rainfall is less than 100 mm.

c.) Find the probability that the yearly rainfall is more than 240 mm.

d.) Find the probability that the yearly rainfall is between 140 and 250 mm.

e.) If a year has a rainfall less than 100mm, does that mean it is an unusually dry year? Why or why not?

f.) What rainfall amount are 90% of all yearly rainfalls more than?

Answer 1

a) Let X denotes the yearly rainfall in Sydney, Australia.

Here

X ~ Normal(137, 69²)

a) The probability that the yearly rainfall is less than 100 mm

c) The probability that the yearly rainfall is more than 240 mm

d) The  probability that the yearly rainfall is between 140 and 250 mm

e) Since probability that the yearly rainfall is less than 100 mm = 0.295899 which is quite significantly different from 0, so it is an unusually dry year.

f) To find the rainfall amount(x) such that 90% of all yearly rainfalls more than x

(ans)