If it is known that the length of time recovered from patients with mild COVID-19 is spread normally with = 14 days and = 2 days. Then 50 samples of patients with mild patients were taken

a. What percentage of these patients will recover between 10 and 20 days

b. Determine a 95% confidence interval for the population mean duration of recovery

The results of observations of 40 samples of positive COVID-19 patients who received treatment at the hospital showed that the average length of recovery was 12 days with a standard deviation of 2 days. Meanwhile, the results of observations of 50 samples of positive COVID-19 patients who were treated independently at home showed that the average length of recovery was 14 days with a standard deviation of 3 days. Hypothesis testing that patients who are hospitalized recover faster than patients treated at home. Give the interpretation (Use = 0.05)!