Sociologists say that 90 of married women claim that their h

Sociologists say that 90% of married women claim that their husband\'s mother is the biggest bone of contention in their marriages (sex and money are lower-rated areas of contention). Suppose that eleven married women are having coffee together one morning. Find the following probabilities. (Round your answers to three decimal places.)

(a) all of them dislike their mother-in-law

(b) none of them dislike their mother-in-law

(c) at least nine of them dislike their mother-in-law

(d) no more than eight of them dislike their mother-in-law

Solution

a)

P(all) = 0.9^11 = 0.313810596 = 0.314 [answer]

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b)

P(non) = (1-0.9)^11 = 0.00000000001 = 0.000 [answer]

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c)

Note that P(at least x) = 1 - P(at most x - 1).          
          
Using a cumulative binomial distribution table or technology, matching          
          
n = number of trials =    11      
p = the probability of a success =    0.9      
x = our critical value of successes =    9      
          
Then the cumulative probability of P(at most x - 1) from a table/technology is          
          
P(at most   8   ) =    0.089561851
          
Thus, the probability of at least   9   successes is  
          
P(at least   9   ) =    0.910438149 = 0.910 [answer]
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d)

Using a cumulative binomial distribution table or technology, matching          
          
n = number of trials =    11      
p = the probability of a success =    0.9      
x = the maximum number of successes =    8      
          
Then the cumulative probability is          
          
P(at most   8   ) =    0.089561851 [answer]