Question

I guessed, on the ones I did.

Answer 1

Standard error $\sigma_M$ = $\sigma /\sqrt{n}$ = $20 /\sqrt{50}$ = 2.83

Average difference between mean number of seats in 559 restaurants and on random sample = E(x - 99.2) = E(x) - 99.2 = M - 99.2 = 103.4 - 99.2 = 4.2

Average difference between mean number of seats in sample of 50 and on random sample = E(x - 103.4) = E(x) - 103.4 = M - 103.4 = 103.4 - 103.4 = 0

Average difference between mean number of seats in 559 restaurants and mean number of seats in sample of 50 = M - $\mu$ = 103.4 - 99.2 = 4.2

z score is,

z = (103.4 - 99.2) / 2.83 = 1.484

P(M > 103.4) = P(z > 1.484) = 0.0689