Question

Statistics from a​ college's climate center indicate that the city the college is in gets an average of 35.9​" of rain each​ year, with a standard deviation of 4.1​". Assume that a Normal model applies. Complete parts a through d below.

The percentage of years with more than 41​" of rain is 10.75​%.

​b) Less than how much rain falls in the driest 20​% of all​ years? The driest 20​% of all years get at most nothing​" of rain.

Answer 1

b)

X ~ N ( µ = 35.9 , σ = 4.1 )
P ( X < x ) = 20% = 0.2
To find the value of x
Looking for the probability 0.2 in standard normal table to calculate critical value Z = -0.8416
Z = ( X - µ ) / σ
-0.8416 = ( X - 35.9 ) / 4.1
X = 32.45"