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Detection of the COVID 19 virus is possible through the reverse transcription-polymerase chain reaction (RT-PCR) kits and computed tomography (CT) images of the lungs. Diagnosis via CT images provides a faster diagnosis than the RT-PCR method does. In addition to low false-negative rate, CT is also used for prognosis in determining the severity of the disease and the proposed treatment method. In this study, we estimated a probability density function (PDF) to examine the infections caused by the virus. We collected 232 chest CT of suspected patients and had them labeled by two radiologists in 6 classes, including a healthy class and 5 classes of different infection severity. To segment the lung lobes, we used a pre-trained U-Net model with an average Dice similarity coefficient (DSC) greater than 0.96. First, we extracted the PDF to grade the infection of each lobe and selected five specific thresholds as feature vectors. We then assigned this feature vector to a support vector machine (SVM) model and made the final prediction of the infection severity. Using the T-Test statistics, we calculated the p-value at different pixel thresholds and reported the significant differences in the pixel values. In most cases, the p-value was less than 0.05. Our developed model was developed on roughly labeled data without any manual segmentation, which estimated lung infection involvements with the area under the curve (AUC) in the range of [0.64, 0.87]. The introduced model can be used to generate a systematic automated report for individual patients infected by COVID-19.