An unnoticed mechanical failure has caused onefourth of a ma

An unnoticed mechanical failure has caused one-fourth of a machine shop

Solution

a) yes np, nq = 6, 18 > 5

n = 25; p = 0.2500; q = 0.7500; P(x = 4) = nCx p^x (1-p)^(n-x) = 0.1175268
x P(x) ?P(x) 1-?P(x)
--- --------- --------- ---------
0 0.0007525 0.0007525 0.9992475
1 0.0062712 0.0070237 0.9929763
2 0.0250848 0.0321085 0.9678915
3 0.0641056 0.0962141 0.9037859
4 0.1175268 0.2137409 0.7862591

binomial gives p(X>4) = 0.7862591

? = (n p) = 6.2500; ?