SOLUTION: Sociologists say that 80% of married women claim that their husband’s mother is the biggest bone of contention in their marriages. Suppose that 5 married women are having coffe

It is a binomial distribution probability problem.


To facilitate my calculations, I will use an appropriate online (free of charge) calculator 
at this web-site 

https://stattrek.com/online-calculator/binomial.aspx


It provides a convenient input (and output) for all relevant options/cases.


(1)  exactly 3 of them dislike their mother-in-law ?

         - number of trials        n = 5;
         - number of success trial k = 3;
         - Probability of success on a single trial p = 0.8.

           P(n=5; k=3; p=0.8) = 0.2048  (rounded).      ANSWER


(2)  all of them dislike their mother-in law?

         - number of trials        n = 5;
         - number of success trial k = 5;
         - Probability of success on a single trial p = 0.8.

           P(n=5; k=5; p=0.8) = 0.3277  (rounded).     ANSWER


(3)  none of them dislike their mother-in-law?

         - number of trials        n = 5;
         - number of success trial k = 0;
         - Probability of success on a single trial p = 0.8.

           P(n=5; k=0; p=0.8) = 0.00032.     ANSWER


(4)  at least 4 of them dislike their mother-in-law?

         - number of trials        n = 5;
         - number of success trial k >= 4;
         - Probability of success on a single trial p = 0.8.

           P(n=5; k>=4; p=0.8) = 0.7373  (rounded).    ANSWER


(5) no more than 3 of them dislike their mother-in-law?

         - number of trials        n = 5;
         - number of success trial k <= 3;
         - Probability of success on a single trial p = 0.8.

           P(n=5; k<=3; p=0.8) = 0.2627  (rounded).     ANSWER


(7)  The expected number of this binomial distribution is n*p = 5*0.8 = 4.

     The standard deviation is  s =  =  = 0.8944  (rounded).