Question

Sociologists say that 85% 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 elevenmarried women are having coffee together one morning. Find the following probabilities. (For each answer, enter a number. 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.

Answer 1

Binomial distribution: P(X) = nCx p^x q^n-x

P(dislike mother-i-law), p = 0.85

q = 1 - 0.85 = 0.15

Sample size, n = 11

a) P(all of them dislike their mother-in-law) = P(11)

= 0.85¹¹

= 0.1673

b) P(none of them dislike their mother-in-law) = P(0)

= 0.15¹¹

= 8.65x10^-10

c) P(at least nine of them dislike their mother-in-law) = P(9) + P(10) + P(11)

= 11C9x0.85⁹x0.15² + 11x0.85¹⁰x0.15 + 0.85¹¹

= 0.7788

d) P(no more than eight of them dislike their mother-in-law) = 1 - P(more than eight of them dislike their mother-in-law)

= 1 - 0.7788

= 0.2212