Let (Y) have a chi-square distribution with 15 degrees of freedom, let (X) have a chi-square distribution

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Let \(Y\) have a chi-square distribution with 15 degrees of freedom, let \(X\) have a chi-square distribution with 5 degrees of freedom, and let \(Y=X+Z\), where \(X\) and \(Z\) are independent random variables.

(a) Calculate \(P(y>27.488)\).

(b) Calculate \(P(6.262

(c) Find \(c\) such that \(P(y>c)=.05\).

(d) Find \(c\) such that \(P(z>c)=.05\).

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