Provide an appropriate response.The standard normal probability density function is defined by f(x) = 
e- x2/2. (a) Use the fact that 
dx = 1 to show that 
dx =
.(b) Use the result in part (a) to show that the standard normal probability density function has variance 1.
What will be an ideal response?
(a) Since 
dx = 1 and f(x) is an even function, 
dx = 
. Then 
dx = 
dx = 
= 
dx = 
.
(b) The variance of the distribution is equal to 
dx = 
dx + 
dx = 
+ 
= 1.
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Answer the question.Which of the following quantities of interest would be most difficult to determine?
A. The percentage of second graders who read above grade level B. The number of children living below the poverty line C. The number of children not counted in the last census D. The percentage of children who brush their teeth at least twice a day
State the domain of the rational expression.
A. {x|x ? 9, x ? -7}
B. {x|x ? -9, x ? -7}
C. {x|x ? 9, x ? -7, x ? 
, x ? 0}
D. {x|x ? 9, x ? -7, x ? 
}
Rewrite the expression without absolute value bars.
A. -6 B. 2 C. -2 D. 6
Add or subtract. Assume all variables represent positive real numbers.11
- 3x
A. 8x
B. 14
C. 11
- 3x
D. 8x