case rate or morbidity rate an inexact term that can mean either the incidence rate or the prevalence ratebesides the time period of analysis one need to define the population (general population, commonly the census population that is easy to obtain)  or the population at risk (much more difficult to determine for some diseases with lifelong or longterm immunity).Case, i assume, is someone with a positive PCR test, they may start including antibody test for those that did not get a PCR test, they try not to double count..3,392 new cases reported for June 27, past week daily counts range from 1,812 to 3,779 per day so there is some reporting noise in the data, weekly might be a better metric.Population, is the general population,  7,278,000 for AZ that is posted on https://covidusa.net/?state=Arizona  (so technically it is prevalence because they are counting those that have had it and are immune, at least for a couple months or more.
so today there is 46.6 new cases per 100,000 (per day)that ranged this past week24.9 to 51.9 new case per 100,000 (per day)
Back calculating ADHS's confusing, unexplained number gives 70,917 cases that they may have used for their "rate.". Suspiciously close to 70,051 that they give for total number of cases (since the beginning I assume). pulled from https://www.azdhs.gov/preparedness/epidemiology-disease-control/infectious-disease-epidemiology/covid-19/dashboards/index.php