Question

kekes kookies (https://kekekookies.com/) sells mini cookies in packs of 5 and has determined a probability distribution for the number of cookies that they sell in a given day.

x = #sold

probability

|----|

0	0.15
5	0.48
10	0.09
15	...?
20	0.15

a. what is the probability of selling 15 mini cookies in a given day?
b. find the expected number of mini cookies sold in a day using the discrete probability distribution.
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Explanation:

Step1: Use probability - sum property

The sum of probabilities in a discrete probability distribution is 1. Let \(P(15)\) be the probability of selling 15 cookies. Then \(0.15 + 0.48+0.09 + P(15)+0.15 = 1\).

Step2: Solve for \(P(15)\)

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Step3: Recall expected - value formula

The formula for the expected value \(E(X)\) of a discrete random variable \(X\) is \(E(X)=\sum_{i}x_ip_i\), where \(x_i\) are the possible values of \(X\) and \(p_i\) are their corresponding probabilities.

Step4: Calculate the expected value

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Answer:

a. 0.13
b. 8.25