N259NMuSigma2 1 Musigma i1 to 6 Xi2529 P136 leq u leq 93 2

N(25,9),N(Mu,Sigma^2) 1) Mu=sigma i=1 to 6 (Xi-25)^2/9 P(1.36) leq u leq 9.3 ? 2) u= sigma i=1 to 6 (Xi-x bar)^2/9 P(2,3 leq u leq 10.3)?

Solution

u = sum of( x1-25)^2 /9 = z1^2 +z2^2+z3^2+....

Each z1 follows a std normal distribution.

Hence u = sum of chi square variables follow a chi square distribution with df = 6-1 =5

P(1.36<=u<=9.3) from the table is 0.9286-0.09768=0.83092

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P(2.3<=u<=10.3) for chi square with df 5 is

=0.8062-0.0672

= 0.7390