Question

5.1 basics of probability distributions. compute the mean and standard deviation of a discrete random variable.
kekos 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
5	0.52
10	0.09
15	...?
20	0.09

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: Find missing probability

Since the sum of all probabilities in a probability - distribution is 1. Let the probability of selling 15 cookies be $p$. Then $0.28 + 0.52+0.09 + p+0.09 = 1$. Solving for $p$ gives $p=1-(0.28 + 0.52+0.09 + 0.09)=0.02$.

Step2: Calculate the expected value

The formula for the expected value $E(X)$ of a discrete random variable is $E(X)=\sum_{i}x_ip_i$. Here, $E(X)=0\times0.28 + 5\times0.52+10\times0.09 + 15\times0.02+20\times0.09$
$=0 + 2.6+0.9 + 0.3+1.8$
$=5.6$.

Answer:

a. 0.02
b. 5.6