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. 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. c. find the variance of the number of mini cookies sold in a day using the discrete probability distribution. question help: message instructor submit question

Question

Accepted Answer

# Explanation:
## Step1: Find probability for 15 cookies
The sum of all probabilities in a probability distribution is $1$. Let $P(X = 15)=p$. Then $0.21+0.13 + 0.2+p+0.18=1$.
$$
\begin{align*}
0.21+0.13+0.2 + 0.18+p&=1\
0.72 + p&=1\
p&=1 - 0.72\
p&=0.28
\end{align*}
$$
## Step2: Calculate expected value $E(X)$
The formula for the expected value of a discrete random variable $E(X)=\sum_{i}x_ip_i$.
$$
\begin{align*}
E(X)&=(0\times0.21)+(5\times0.13)+(10\times0.2)+(15\times0.28)+(20\times0.18)\
&=0 + 0.65+2+4.2 + 3.6\
&=10.45
\end{align*}
$$
## Step3: Calculate variance $V(X)$
First, calculate $E(X^{2})=\sum_{i}x_{i}^{2}p_i$.
$$
\begin{align*}
E(X^{2})&=(0^{2}\times0.21)+(5^{2}\times0.13)+(10^{2}\times0.2)+(15^{2}\times0.28)+(20^{2}\times0.18)\
&=0+3.25 + 20+63+72\
&=158.25
\end{align*}
$$
The formula for variance $V(X)=E(X^{2})-(E(X))^{2}$.
$$
\begin{align*}
V(X)&=158.25-(10.45)^{2}\
&=158.25 - 109.2025\
&=49.0475
\end{align*}
$$

# Answer:
a. $0.28$
b. $10.45$
c. $49.0475$

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QUESTION IMAGE

Question

Explanation:

Step1: Find probability for 15 cookies

Step2: Calculate expected value \(E(X)\)

Step3: Calculate variance \(V(X)\)

Answer: