Question

The weights of loaves of rye bread at a bakery are normally distributed with a mean of 16 oz and a standard deviation of 0.5 oz. The bakery produces 120 loaves of rye bread each day. About how many loaves each day are expected to weigh between 16 oz and 16.5 oz?

Answer 1

Let
`X` be the weight of any given loaf. Then


`\mathbb P(16<X<16.5)=\mathbb P\left((16-16)/(0.5)<(X-16)/(0.5)<(16.5-16)/(0.5)\right)=\mathbb P(0<Z<1)`

where
`Z` follows the standard normal distribution. Because the distribution is symmetric,


`\mathbb P(0<Z<1)=\mathbb P(Z<1)-\mathbb P(Z<0)\approx0.3413`

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.