Guidelines to problems
chapter 6
Nutan S. Mishra
Department of Mathematics and Statistics
University of South Alabama
Exercise 6.26
Draw a picture of the z-curve before computing each probability.
a.
p(z > -1.06)= area to the right side of z= -1.06
= p(z < 1.06)= which is same as area to the left of z= 1.06
b.
p(-.68  z  1.84) = area between -.68 and 1.84.
Since -.64 is on the left of 0 and 1.84 is to the right of 0, we add the
two areas to compute the total area
= p(0< z < 1.84) + p( 0< z <.68)
c.
p(0  z  3.85) = area between 0 and 3.85.Since area covered
between 0 and 3.09 is .4990 which is close to .5
We conclude that area between 0 and 3.85 is almost .5
and hence p(0  z  3.85)  .5
d.
p(-4.34 z  0) = area between 0 and -4.34
=p (0  z  4.34)= which is same as area between 0 and 4.34
 .5 ( by the same argument as in part c)
e.
p(z > 4.82 ) = 1-p(z < 4.82)  0 (write the explanations and draw
curve)
f.
p(z < -6.12) = p( z > 6.12)  0 (same argument as in part c)
Exercise 6.36
Given that x~ N(65, 15)
43  65
a. p(x<43) = p( z < 15 ) = p(z < -1.47)=p(z > 1.47)
74  65
b. p(x>74) = p(z > 15 ) = p(z > .6)
c. p(x> 56) = p(z > 56  65 ) = p( z > -.6) = p(z < .6)
15
d. p(x < 71) = p(z < .4)
Draw the picture of z-curve for each of above and
then find the probabilities from normal table.
Exercise 6.48
X = stress score of a dental patient
X ~ N(7.59, .73)
a. Percentage of the patients with stress score less than
6.00 = 100* p(x < 6.0)
=100* p( z < 6.0  7.59 )
.73
b.
= 100* p( 7.0 < x < 8.0)
= 100* p( 7.0  7.59 < z < 8.0  7.59 )
.73
c.
.73
A patient needs sedative if her stress score is more
than 9.0
Percentage of the patients that would need sedative
100* p(x > 9.0) = 100*p( z > 6.0  7.59 )
.73
Exercise 6.52
X= weight of a hockey puck in ounces
X ~ N(5.75, .11)
Specifications given by NHL for weight of the puck
is 5.5<x<6.0
Percentage of pucks can not be used by NHL=
percentage of the pucks falling outside the
specification limits
= 100* p(x<5.5 or x>6.0)
=100* {p(x<5.5) + p(x>6.0)
=100* {p(z<____) +p(z> ____)
Complete this problem
Exercise 6.58
It is given that X~N(550, 75)
a. p(X< x )= .0250
= p(Z<z) = .0250
First find the value of -z
Using the normal table
Then use the transformation
formula to find the
corresponding value of x
x = µ+ zσ
Exercise 6.58 part b
p(X>x) = .9345
p(Z>z) = .9345
First find the value of -z
Using the normal table
Then use the transformation
formula to find the
corresponding value of x
x = µ+ zσ