Let [tex]X[/tex] be the weight of any given loaf. Then
[tex]\mathbb P(16<X<16.5)=\mathbb P\left(\dfrac{16-16}{0.5}<\dfrac{X-16}{0.5}<\dfrac{16.5-16}{0.5}\right)=\mathbb P(0<Z<1)[/tex]
where [tex]Z[/tex] follows the standard normal distribution. Because the distribution is symmetric,
[tex]\mathbb P(0<Z<1)=\mathbb P(Z<1)-\mathbb P(Z<0)\approx0.3413[/tex]
which means approximately 34.13% of the loaves baked daily should be expected to weigh between 16 and 16.5 oz. Out of 120 total loaves, that proportion amounts to 40.956, or approximately 41 loaves.
