One hundred volunteers who have agoraphobia (fear of open and crowded space) are available for a study. Fifty are selected at random and are given the drug imipramine, which is believed to be effective in treating agoraphobia. The other 50 are given a placebo. A psychiatrist evaluates the symptoms of all volunteers after two months to determine if there has been substantial improvement in the severity of their symptoms. What type of study is this?
A. Matched pair design
B. Observational study
C. Completely randomized block design
D. Completely randomized design

Intermediate value theorem
(j. stewart, “calculus”, 7th ed., brook/coles.)

if you have a function  that's is continuous on a closed interval  , and a number  is an intermediate value between  and  , then there's some number  in the interval  that satisfies .



the c is for  the x-value or the input value into the function.
the k is for the y-value or the output value of the function at c.

so in this question, we have a continuous function  on  . the interval in question for the ivt must be  then.

k is between the values of the function at the endpoints. so 

so for  , we need to get the values of the function at the endpoints of the interval to determine the range that k can be in.

   

   

and c must be a number in the interval  . (your current answers of  goes out of the interval originally stated for the function. the c is the x-value or the input value into the function.)

so for every    in  , there is a  in  etc.. though i don't know about how many decimal places to round to  for