Some customers do not plan ahead, so every day, the bakers at All About Cakes ba

Question

Some customers do not plan ahead, so every day, the bakers at All About Cakes bakery produce four cakes for last minute emergency orders. If the cakes are not sold within two days, they are thrown out. Each cake costs $10 in supplies and overhead, and it sells for $25. The probability distribution for the number of cakes sold out of each batch of four is given below. Find the expected profit for the bakery generated from these batches of four cakes. (Hint: For every unsold cake, the bakery loses $10. For every sold cake the bakery earns $15 in profit.)

Do not round intermediate calculations. Enter your answer as a decimal rounded to two places.

Expected profit = ____ dollars

Explanation / Answer

Expected number of cakes sold

= 0 * 0.03 + 1 * 0.12 + 2 * 0.28 + 3 * 0.38 + 4 * 0.19

= 2.58

Profit for a cake sold = $25 - $10 = $15.

=> Expected profit = $15 * 2.58

= $38.7.

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