The probabilities that a surgeon operates on 3, 4, 5, 6, or 7 patients in any one day are 0.15, 0.20, 0.25, 0.20 and 0.20, respectivel

The average number of patients that a surgeon operates on a day is same as finding the mean number of patients that a surgeon operates given as,

$E(x)=\sum xp(x)=(3\times 0.15)+(4\times 0.20)+(5\times 0.25)+(6\times 0.20)+(7\times0.20)=0.45+0.80+1.25+1.2+1.4=5.1\approx 5$ Therefore, the average number of patients that a surgeon operates in a day is approximately 5 patients.