document.write( "Question 1198224: 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 together one morning. What is the probability that :\r
\n" ); document.write( "\n" ); document.write( "1 exactly 3 of then dislike their mother- in law ?
\n" ); document.write( "2 all of them dislike their mother- in law ?
\n" ); document.write( "3 none of them dislike their mother -in law?
\n" ); document.write( "4 at least 4 of them dislike their mother in law?
\n" ); document.write( "5 no more than 3 of them dislike their mother in law ?
\n" ); document.write( "7 what is the expected number of women who dislike their mother in law ? What is the standard deviation of the distribution? \n" ); document.write( "
Algebra.Com's Answer #831782 by ikleyn(52805)\"\" \"About 
You can put this solution on YOUR website!
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\n" ); document.write( "Sociologists say that 80% of married women claim that their husband’s mother
\n" ); document.write( "is the biggest bone of contention in their marriages.
\n" ); document.write( "Suppose that 5 married women are having coffe together one morning.
\n" ); document.write( "What is the probability that :
\n" ); document.write( "(1) exactly 3 of then dislike their mother- in law ?
\n" ); document.write( "(2) all of them dislike their mother- in law ?
\n" ); document.write( "(3) none of them dislike their mother -in law?
\n" ); document.write( "(4) at least 4 of them dislike their mother in law?
\n" ); document.write( "(5) no more than 3 of them dislike their mother in law ?
\n" ); document.write( "(7) what is the expected number of women who dislike their mother in law ?
\n" ); document.write( " What is the standard deviation of the distribution?
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document.write( "It is a binomial distribution probability problem.\r\n" );
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document.write( "To facilitate my calculations, I will use an appropriate online (free of charge) calculator \r\n" );
document.write( "at this web-site \r\n" );
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document.write( "https://stattrek.com/online-calculator/binomial.aspx\r\n" );
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document.write( "It provides a convenient input (and output) for all relevant options/cases.\r\n" );
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document.write( "(1)  exactly 3 of them dislike their mother-in-law ?\r\n" );
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document.write( "         - number of trials        n = 5;\r\n" );
document.write( "         - number of success trial k = 3;\r\n" );
document.write( "         - Probability of success on a single trial p = 0.8.\r\n" );
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document.write( "           P(n=5; k=3; p=0.8) = 0.2048  (rounded).      ANSWER\r\n" );
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document.write( "(2)  all of them dislike their mother-in law?\r\n" );
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document.write( "         - number of trials        n = 5;\r\n" );
document.write( "         - number of success trial k = 5;\r\n" );
document.write( "         - Probability of success on a single trial p = 0.8.\r\n" );
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document.write( "           P(n=5; k=5; p=0.8) = 0.3277  (rounded).     ANSWER\r\n" );
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document.write( "(3)  none of them dislike their mother-in-law?\r\n" );
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document.write( "         - number of trials        n = 5;\r\n" );
document.write( "         - number of success trial k = 0;\r\n" );
document.write( "         - Probability of success on a single trial p = 0.8.\r\n" );
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document.write( "           P(n=5; k=0; p=0.8) = 0.00032.     ANSWER\r\n" );
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document.write( "(4)  at least 4 of them dislike their mother-in-law?\r\n" );
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document.write( "         - number of trials        n = 5;\r\n" );
document.write( "         - number of success trial k >= 4;\r\n" );
document.write( "         - Probability of success on a single trial p = 0.8.\r\n" );
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document.write( "           P(n=5; k>=4; p=0.8) = 0.7373  (rounded).    ANSWER\r\n" );
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document.write( "(5) no more than 3 of them dislike their mother-in-law?\r\n" );
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document.write( "         - number of trials        n = 5;\r\n" );
document.write( "         - number of success trial k <= 3;\r\n" );
document.write( "         - Probability of success on a single trial p = 0.8.\r\n" );
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document.write( "           P(n=5; k<=3; p=0.8) = 0.2627  (rounded).     ANSWER\r\n" );
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document.write( "(7)  The expected number of this binomial distribution is n*p = 5*0.8 = 4.\r\n" );
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document.write( "     The standard deviation is  s = \"sqrt%28p%2An%2A%281-p%29%29\" = \"sqrt%280.8%2A5%2A%281-0.8%29%29\" = 0.8944  (rounded).\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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\n" ); document.write( "\n" ); document.write( "Do not think that this problem is very original. Similar problems come often to this forum.\r
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\n" ); document.write( "\n" ); document.write( "See, for example, this link\r
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\n" ); document.write( "\n" ); document.write( "https://www.algebra.com/algebra/homework/Probability-and-statistics/Probability-and-statistics.faq.question.1160081.html\r
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\n" ); document.write( "\n" ); document.write( "(it came couple of years ago . . . )\r
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