Question

Sociologists say that 80% 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 twelve married 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) At least ten of them dislike their mother-in-law.

(d) No more than nine of them dislike their mother-in-law.

Answer 1

Solution:

Given that p =0.80

n = 12

a)

Mean = Expected Value = μ_x̅ = n•p = (12)(0.8) = 9.60

n•p•(1 - p) = (12)(0.8)(1 - 0.8) = 1.92

Standard Deviation = σ_x̅ = √ n•p•(1 - p) = √1.92 = 1.3856


Finding probability of getting exactly 12 success(es):

Using Binomial Distribution: P(X = 12) = 0.069

b)

Mean = Expected Value = μ_x̅ = n•p = (12)(0.8) = 9.60

n•p•(1 - p) = (12)(0.8)(1 - 0.8) = 1.92

Standard Deviation = σ_x̅ = √ n•p•(1 - p) = √1.92 = 1.3856

Finding probability of getting at least 10 success(es):

Using Binomial Distribution: P(X ≥ 10) = 0.558

c) Mean = Expected Value = μ_x̅ = n•p = (12)(0.8) = 9.60

n•p•(1 - p) = (12)(0.8)(1 - 0.8) = 1.92

Standard Deviation = σ_x̅ = √ n•p•(1 - p) = √1.92 = 1.3856

Finding probability of getting at most 9 success(es):

Using Binomial Distribution: P(X ≤ 9) = 0.442