Answer :
Answer:
ai) P(X=10) in Japan = 0.5988
aii) P(X=10) in the Unites States = 0.00605
bi) Expected value of guilty cases in Japan = 9.5 cases out of 10
Expected value of guilty cases in the United States = 6 cases out of 10
bii) Standard deviation for Japan = 0.689
Standard deviation for the United States = 1.549
Step-by-step explanation:
Probability of being found guilty in Japan = 95% = 0.95
Probability of being found guilty in the United States = 60% = 0.60
a) Probability that 10 court cases are all guilty in Japan is a binomial distribution problem.
Binomial distribution function is represented by
P(X = x) = ⁿCₓ pˣ qⁿ⁻ˣ
n = total number of sample spaces = number of criminals studied = 10
x = Number of successes required = number of guilty cases required = 10
p = probability of success = probability of being found guilty = 0.95
q = probability of failure = probability of not being found guilty = 1 - 0.95 = 0.05
P(X=10) = ¹⁰C₁₀ (0.95)¹⁰ (0.05)⁰= 0.5988
aii) Probability that 10 court cases are all guilty in the United States too is a binomial distribution problem.
n = total number of sample spaces = number of criminals studied = 10
x = Number of successes required = number of guilty cases required = 10
p = probability of success = probability of being found guilty = 0.60
q = probability of failure = probability of not being found guilty = 1 - 0.60 = 0.40
P(X=10) = ¹⁰C₁₀ (0.60)¹⁰ (0.40)⁰= 0.00605
bi) Expected value is given as E(X) = Σ xᵢpᵢ
Summation of all variables and their probabilities.
Expected value in Japan = mean = np = 0.95 × 10 = 9.5 guilty people out of 10
Expected value in the United States = np = 0.6 × 10 = 6 guilty people out of 10
bii) Standard deviation = √(variance)
Variance = np(1-p)
For Japan, Standard deviation = √[10×0.95×0.05] = 0.689
For the United States, Standard deviation =√(10×0.6×0.4) = 1.549