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How Large is the Iceberg? New Evidence from Kansas City

The details are currently vague, but I have tried to report key information, as this is one of the few efforts at random sampling that I am aware of. My main hope is to inspire someone with more expertise and ability to access details to expand the analysis.

Johnson County, with a population of 602k, has reported on preliminary results from an effort to test a representative sample of its residents. I have been unable to find details about how they constructed the sample, so cannot assess how representative it is likely to be, but at least it's not another dataset that selects on the sick. Out of 369 residents tested via PCR on Friday April 10th, 14 residents tested positive, for an estimated infection rate of 3.8%. The results were discussed at the 4/16 Board of County Commissioners Meeting. The video and slides are generally made available at some point after the meeting at https://boccmeetings.jocogov.org/onbaseagendaonline, but they have not been posted as I write this.

Hazarding to Interpret the Results:
Major Caveats
-I don't know how representative the tested sample is of the Johnson County population.
-I don't know details about the type of test they used, so I am not trying to account for false negatives or false positives.
-The test is not for antibodies, so it does not capture people who were infected and recovered.
-I'm ignoring statistical uncertainty.
-The results are from 6 days ago.
-Deaths and hospitalizations from those testing positive will increase with time.

As of April 16, 343 people have tested positive in Johnson County according to the county's dashboard (available at https://public.tableau.com/profile/mapper.of.the.day.mod.#!/vizhome/covid19_joco_public/Dashboard). Ignoring the major caveats above, there should be 22,800 infections in Johnson County, suggesting that:

Infections are being undercounted by a factor of more than 60.
An estimate of infection fatality rate is .1%.
An estimate rate of admission to ICU is .2%
An estimate of the hospitalization rate (inpatient and outpatient) is 1.6%