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Solutions for Lecture Problems from Section 6.2
19.Let
x
be the continuous r.v. of the rainfall (in inches) in Dallas, Texas,
during April.
Given:
μ
= 3.5 in
σ
= 0.8 in
x
is normal
a.
Want
Prob
(
x
> 5 in)
5.0 3.5
1.88
.8
z

=
≈
Prob
(
x
> 5.0)
=
Prob
(
z
> 1.88)
= 1 –
Prob
(
z
< 1.88)
= 1 – 0.9699
= 0.0301
The rainfall exceeds 5 inches in 3.01% of all Aprils.
b. Want
Prob
(
x
< 3 in)
3 3.5
.63
.8
z

=
≈ 
Prob
(
x
< 3.0)
=
Prob
(
z
< 0.63) = 0.2643
Also note that by the symmetry of the normal curve
Prob
(
z
< 0.63) =
Prob
(
z
> 0.63)
= 1 –
Prob
(
z
< 0.63)
= 1 – 0.7357
= 0.2643
The rainfall is less than 3 inches in 26.43% of all Aprils.
c.
“Extremely wet” month if total April rainfall is in the upper 10% of
the distribution.
Want the value of
x
* so that
Prob
(
x
≥
x
*) = 0.10
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View Full DocumentTop 10% of rainfall in all Aprils means upper 10% of the normal
curve, in the right tail.
Right tail area =
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 Fall '08
 SINGER

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