Question 387293
a.  n = 36, this is considered a large sample.  For large samples, the Central Limit Theorem says that the distribution of the sample means is approximately normal (getting better as n gets higher and higher).  The mean is {{{mu = 40}}}and the variance {{{((sigma)_X)^2 = sigma^2/n}}}.

b.  {{{P(X > 43) = P((X - 40)/(18/sqrt(36)) > (43 - 40)/3 = 1)}}}.  Hence {{{P(X > 43) = P(Z > 1) = 0.1587}}}.

c. {{{P(X < 34) = P((X - 40)/(18/sqrt(36))> (34 - 40)/3 = -2)}}}.  Hence {{{P(X < 34) = P(Z < -2) = 0.0228}}}.