The top chart is from a Pew Research Center survey done between October 2nd and 5th of a random national sample of 1,007 adults, with a 3.6 point margin of error.
The second chart is from a Gallup Poll done on October 4th and 5th of a random national sample of 1,016 adults, with a margin of error of 4 points.
Both of the polls show the same thing (and therefore tend to verify each other) -- that between 37% and 41% of the general public (or around 4 out of every 10 Americans) doesn't really trust the federal government (i.e., the CDC) to properly handle an outbreak of the Ebola virus in this country.
Those polls celebrated the positive aspect -- that a majority did trust the CDC (and were not worried about catching the Ebola virus). I found it more interesting that such a significant minority did not trust the CDC, because I was surprised that it was as large as about 40%.
It is generally recognized that the Center for Disease Control (CDC) in the United States is among the best in the world (if not the best). Why do so many doubt their ability to control an outbreak of Ebola in this country? This is especially puzzling, since Ebola is not an airborne virus (which you can get from someone sneezing or coughing in the same room). You must actually have contact with a sick person's blood or other bodily fluids (and even then, the person is not contagious until they start showing symptoms).
This reminds me of the irrational fear in the general public when AIDS first became widely know. People were told that AIDS patients were not a danger (unless you were planning to swap bodily fluids with them), but people overreacted in spite of being told that -- and they went to ridiculous lengths to avoid those patients. Maybe it's just natural for Americans to go off the deep end when a new danger is exposed. And it doesn't have to be a disease -- since we have overreacted to the threat from terrorism also, even though it is still a minor threat in this country (since we have a greater chance of dying from scores of other things).