Suppose that a commercial bakery produces chocolate chip cookies. Based on extensive testing, the bakery has determined that the ideal number of chocolate chips per cookie is 18. In the past, master bakers mixed the dough and spooned it onto sheet pans by hand, but the owners have decided to test a new machine.

The machine extrudes dough onto baking sheets at a uniform rate. It runs continuously from 5:30 a.m. until 1:30 p.m. The number of chips per cookie depends on the viscosity of the dough, and because the dough stiffens as it sits in the machine, the machine produces cookies that contain the optimal number of chips, 18 per cookie, between the hours of 6:00 a.m. and 11 a.m. The distribution of cookies is shown in the graph below.

Based on the times that the machine produces cookies that have the optimal amount of chips, the proportion produced daily with the optimal number of chips is 62.5% or 0.625.

What is the proportion of cookies with optimal chocolate chips?

This can be found by the formula:

= (Hours that optimal cookies are produced) / Hours that the machine runs per day

5:30 am is the same as 5.5 hours because 30 minutes is half an hour.

1:30 pm is also the same as 13.5 hours by the above rule and in 24 hour notation.

Proportion of optimal cookies is therefore:

= (11 am - 6am) / (13.5 - 5.5)

= 5 / 8

= 0.625

= 62.5%

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