Question 1175123
This is 0.85^5=0.4437
-
fewer than 2 is 1 or 0
probability of 0 fixed is 0.15^5=0.00008 plus p(1)=5C1*0.85^1*0.15^4=0.0022.  The sum is 0.0230 prob.
-
at least 3: probability of 2 being fixed is 5C2*0.85^2*0.15^3=0.0244. Add that to the above answer and get 0.0266. At least 3 is 1- prob of (0, 1, 2) or 0.9734. Can use calculator to get right sided probability by doing 1-probability of the left side, so 1-binomcdf(5,.85,2) will give the probability of greater than 2, which is the same as at least 3.
-
mean is np=4.25 troubles.