Answer
a. $0.7734$
b. $0.0521$
c. $0.3802$
d. $65$ inches.
Work Step by Step
Given $\mu=49,\sigma=8$,
We can find the probability that next year
Greenville will receive the following amount of rainfall.
a. At most 55 inches of rain
$z1=\frac{55-49}{8}=0.75,P(X\leq55)=P(z1)=0.7734$
b. At least 62 inches of rain
$z2=\frac{62-49}{8}=1.625,P(X\geq62)=1-P(z2)=1-0.9479=0.0521$
c. Between 46 and 54 inches of rain
$z3=\frac{46-49}{8}=-0.375,z4=\frac{54-49}{8}=0.625,
P(46\lt X\lt54)=P(z4)-P(z3)=0.7340-0.3538=0.3802$
d. An extremely wet year can be defined as a rain amount far away from the mean to the right,
in this case 2 standard deviations. Thus, $z=\frac{X-49}{8}=2$, and we can solve for $X=65$ inches.
