5.1 basics of probability distributions. compute the mean and standard deviation of a discrete random…

5.1 basics of probability distributions. compute the mean and standard deviation of a discrete random variable.\nkekos 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.\n|x = #sold|probability|\n|----|----|\n|0|0.28|\n|5|0.52|\n|10|0.09|\n|15|...?|\n|20|0.09|\na. what is the probability of selling 15 mini cookies in a given day?\nb. find the expected number of mini cookies sold in a day using the discrete probability distribution.\nquestion help: message instructor post to forum

5.1 basics of probability distributions. compute the mean and standard deviation of a discrete random variable.\nkekos 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.\n|x = #sold|probability|\n|----|----|\n|0|0.28|\n|5|0.52|\n|10|0.09|\n|15|...?|\n|20|0.09|\na. what is the probability of selling 15 mini cookies in a given day?\nb. find the expected number of mini cookies sold in a day using the discrete probability distribution.\nquestion help: message instructor post to forum

Answer

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