Math 370 HW 3 - Homework3 3-43, 3-44, 3-50, 3-57, 3-62,...

1
Homework3
3-43, 3-44, 3-50, 3-57, 3-62, 3-63
3-43. a) P(X < 31) = P(Z < -3) = 0.001350
b) P(X > 30) = P(Z > -3.5) = 0.999767
c) P(33 < X < 37) = P(-2 < Z < 0) = P(Z < 0) – P(Z < -2) = 0.5 – 0.02275 = 0.47725
d) P(32 < X < 39) = P(-2.5 < Z < 1) = 0.841345 – 0.00621 = 0.835135
e) P(30 < X < 38) = P(-3.5 < Z < 0.5) = 0.691462 – 0.000233 = 0.691229
3-44. a) P(X > x) = 1 – P(X < x)
= 1 -





 

3
6 x
Z P
= 0.50.
And,





 

3
6 x
Z P
= 0.50
Therefore,
3
6 x 
= 0 and x = 6.
b) P(X > x) = 1 – P(X < x)
= 1 -





 

3
6 x
Z P
= 0.95.
And,








3
6 x
Z P
= 0.05
Therefore,
3
6 x 
= -1.645 and x = 1.065.
c) P(x < X < 9) = 0.20
641345 . 0
3
6 x
Z P
20 . 0 841345 . 0
3
6 x
Z P
20 . 0
3
6 x
Z P 841345 . 0
20 . 0
3
6 x
Z P ) 1 Z ( P
1 Z
3
6 x
P
3
6 9
Z
3
6 x
P









  




 

 




 
 








  






 

 




 
 


2
Therefore,
3
6 x 
=0.36, and x = 7.08.
d) P(3 < X < x) = 0.80
P Z
x
P Z
x
P Z
x
P Z
P Z
x
P Z
x
3 6
3
6
3
1
6
3
6
3
1 080
6
3
0158655 080
6
3
0 958655

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