Question 923682
μ = 45 and σ = 3.2 inches 
(a) If an individual kindergarten child is selected at random, what is the probability that he or she has a height between 42.7 and 47.3 inches? 
{{{z = blue(x - mu)/blue(sigma)}}}    
P(42.7< x < 47.3) = P( -2.3/3.2 < z < 2.3/3.2) = normalcdf(-.7188, .7188)
............
 {{{z =blue (x - mu)/blue(sigma/sqrt(n))}}}
P(42.7< xbar < 47.3) = P(-2.3/.64 < z < 2.3/.64) = normalcdf( -3.5938, 3.5938)
.......
P( x > 47.2) = P(z > 2.2/3.2) = normaldcdf( .6875, 100)
.......
P( xbar > 47.2) = P(z > 2.2/.64) = normalcdf(3.4375, 100)