SOLUTION: In a certain state in the USA, “irreconcilable differences” is given as the legal reason in 70% of all divorce cases. Find the probability that in the next 20 divorce cases fi

Question 1197447: In a certain state in the USA, “irreconcilable differences” is given as the legal reason in 70% of all divorce cases. Find the probability that in the next 20 divorce cases filed in this state,
(a) at least 18 will claim “irreconcilable differences” as the reason.
(b) exactly 14 will claim “irreconcilable differences” as the reason.
(c) Find the mean and variance of the number of divorce cases that cite “irreconcilable differences” as the reason for divorce.
Answer by ewatrrr(24785) (Show Source): You can put this solution on YOUR website!


Hi 
Binomial Distribution: p(ir) = .7 and  q(NOt ir) = .3,  n = 20
Using TI or similarly an inexpensive calculator like an Casio fx-115 ES plus
P(x  ≥  18) = 1 - p(x ≤ 17) = 1 - binomcdf( 17,20,.7) = 1 - .9645 = .0355

P(x= 14) = binompdf( 17,20,.7 0) = .0716
Or 
 = .0716

(c) Find the mean and variance of the number of divorce cases that cite “irreconcilable differences” as the reason for divorce.
  mean = np = 20*.7 = 14
Variance = npq = 14*.3 = 4.2
Wish You the Best in your Studies.

RELATED QUESTIONS
In a certain city district, the need for money to buy drugs is given as the reason for... (answered by mathmate)

Forty-three percent of marriages end in divorce. You randomly select 150 married couples. (answered by Boreal)

6. Dewey, Cheetum, and Howe is a law firm that handles divorce cases. A previous study... (answered by stanbon)

The human resources division in a large government department has shown that illness is... (answered by Boreal)

1.Find the uniform distribution for the subsets of months of size 3. 2. Find the... (answered by ikleyn)

A marriage counselor has traditionally seen that the proportion of all married couples... (answered by math_tutor2020)

In a city of 180,000 there are 20,000 legal immigrants from Latin America. What is the... (answered by stanbon)

Forty-three percent of marriages end in divorce. You randomly select 15 married couples.... (answered by math_tutor2020,ewatrrr)

If the paired differences are normal in a test of mean differences, the distribution used (answered by stanbon)