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

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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) About Me  (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.