Please be thorough in your work and explain using English wo

Please be thorough in your work and explain using English words as well. Show all work

(1) Given a=0.01, Z(0.01) =2.33 (from standard normal table)

2.33= (xbar-mu)/(s/vn) = (xbar-4)/(5/sqrt(25))

--> 2.33 = xbar-4

So xbar = 4+2.33=6.33

So the probability of Type II error is

P(X>6.33) = P(Z>(6.33-2)/(5/sqrt(25))

=P(Z>4.33) =0 (from standard normal table)

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(2) Z(0.05/2)= Z(0.025) = 1.96 (from standard normal table)

Z(0.05)=1.65 (from standard normal table)

So n=S^2*(Z(1-a/2) + Z(1-0.95))^2/(4-2)

=5^2*(1.96+1.65)^2/2

=162.9013

Take n=163