Suppose that a commercial bakery produces chocolate chip cookies. Based on exten

Question

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 6:00 a.m. until 2:00 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 6:30 a.m. and 11 a.m. The distribution of cookies is shown in the graph below.

The shaded area represents the proportion of all cookies that contain exactly 18 chocolate chips. 6:00 7:00 8:009:0010:00 1:00 12:00 1:002:00

Explanation / Answer

Proportion of cookies produced each day that contain the optimal number of chocolate chips = Proportion of cookies produced between  6:30 a.m. and 11 a.m

= Number of hours for which cookies containing optimum number of chips are produced / Total number of hours the machine is operated

= (11-6.5)/(14-6)

= 4.5/8

= 56.25%

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