i need a full explanation as to how to do this i am stuck an

i need a full explanation as to how to do this i am stuck and need to figure this out

Solution

x~bin(20,0.25)

qA
P(0) = 0.003171212
P(1) = 0.02114141
P(2) = 0.06694781
P(3) = 0.1338956
P(4) = 0.1896855
P(5) = 0.2023312 <-------- ans to [ C ]
P(6) = 0.1686093
P(7) = 0.1124062
P(8) = 0.06088669
P(9) = 0.02706075
P(10) = 0.009922275
P(11) = 0.00300675
P(12) = 0.0007516875
P(13) = 0.0001541923
P(14) = 0.00002569872
P(15) = 0.000003426496
P(16) = 3.569266e-7
P(17) = 2.799425e-8
P(18) = 1.555236e-9
P(19) = 5.456968e-11
P(20) = 0

qB
add up suitably

qD
E[x] = np = 20*0.25 = 5

qE
? = sqrt(npq) = sqrt(20*0.25*0.75) = 1.93649 <-----