Let X_1, X_2, ..., X_21 be a random sample from a normal distribution with µ =...

Question

Question

Let X_1, X_2, ..., X_21 be a random sample from a normal distribution with µ = 10, σ^2 = 4. Using the chi-square distribution, find P(2 < S^2 < 8)

Answer 1

Answer #1

for we know that (n-1)s²/ σ ² follows chi distribution with n-1 degree of freedom

therefore P(2<S²<8)=P(2*(21-1)/4<(n-1)*s²/σ² <8*(21-1)/4)=P(10<X² <40)=0.9950-0.0318=0.9632

Answer 2

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