Question

The summer monsoon rains in a country follow approximately a Normal distribution with mean 853 millimeters (mm) of rainfall and standard deviation 88 mm. (Round your answers to two decimal places.)

(a) In a drought year, 694 mm of rain fell. In what percent of all years will this country have 694 mm or less of monsoon rain?

(b) "Normal rainfall" means within 20% of the long-term average, or between 682 mm and 1024 mm. In what percent of all years is the rainfall normal?

Answer 1

This is a normal distribution question with

a)

x = 694

P(x < 694.0)=?

The z-score at x = 694.0 is,

z = -1.8068

This implies that

P(x < 694.0) = P(z < -1.8068) = \textbf{0.0354}

b) x1 = 682

x2 = 1024

P(682.0 < x < 1024.0)=?

This implies that

P(682.0 < x < 1024.0) = P(-1.9432 < z < 1.9432) = P(Z < 1.9432) - P(Z < -1.9432)

P(682.0 < x < 1024.0) = 0.9740- 0.0260

P(682.0 < x < 1024.0) = {0.948}= 94.8%

PS: you have to refer z score table to find the final probabilities.

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