The failure rate in a statistics class is 20%. In a class of 50 students, find the probability that less than eight students will fail.

Question

The failure rate in a statistics class is 20%. In a class of 50 students, find the probability that less than eight students will fail. Pleaseeeee I need HELPPPP

Answer 1

It is binomial distribution with p=0.2, n=50, k = 0,1,2,3,...7

 

The formula is  SUM [    (n choose k) p^k (1-p)^(n-k) ] for k=0,1,2,3,4,5,6,7

 

               where N choose k = n!/(k! * (n-k)!)

 

 

             SUM [ ( 50 choose k) (0.2)^k (0.8) ^ (50-k) ] for k=0,1,2,3,4,5,6,7

 

 

The result is just over 19% per the following table, per MS Excel

 

k      50 choose k      (0.2)^k      (0.8)^(50-k)      Probability
0              1                   1            1.42725E-05   1.42725E-05
1              50                0.2           1.78406E-05   0.000178406
2             1225             0.04          2.23007E-05   0.001092737
3             19600           0.008        2.78759E-05    0.004370946
4             230300         0.0016       3.48449E-05    0.012839654
5             2118760      0.00032      4.35561E-05     0.029531204
6           15890700      0.000064     5.44452E-05     0.055371008
7            99884400     0.0000128    6.80565E-05    0.087011584

                                                                   TOTAL 0.190409812