the owner of a local movie theater keeps track of the number of tickets sold in each purchase and makes a probability distribution based on these records. let x represent the number of tickets bought in one purchase. the distribution for x is given in the table. what is the standard deviation of the distribution? 0.89 0.95 1.41 1.99

Question

Accepted Answer

# Explanation:
## Step1: Calculate the expected value $E(X)$
The formula for the expected value of a discrete random variable is $E(X)=\sum_{i}x_ip_i$.
$$
\begin{align*}
E(X)&=(1\times0.29)+(2\times0.44)+(3\times0.19)+(4\times0.06)+(5\times0.02)\
&=0.29 + 0.88+0.57 + 0.24+0.1\
&=2.08
\end{align*}
$$
## Step2: Calculate $E(X^{2})$
The formula for $E(X^{2})=\sum_{i}x_{i}^{2}p_i$
$$
\begin{align*}
E(X^{2})&=(1^{2}\times0.29)+(2^{2}\times0.44)+(3^{2}\times0.19)+(4^{2}\times0.06)+(5^{2}\times0.02)\
&=(1\times0.29)+(4\times0.44)+(9\times0.19)+(16\times0.06)+(25\times0.02)\
&=0.29+1.76 + 1.71+0.96+0.5\
&=5.22
\end{align*}
$$
## Step3: Calculate the variance $\text{Var}(X)$
The formula for the variance of a discrete random variable is $\text{Var}(X)=E(X^{2})-(E(X))^{2}$
$$
\begin{align*}
\text{Var}(X)&=5.22-(2.08)^{2}\
&=5.22 - 4.3264\
&=0.8936
\end{align*}
$$
## Step4: Calculate the standard deviation $\sigma$
The formula for the standard deviation is $\sigma=\sqrt{\text{Var}(X)}$
$$
\sigma=\sqrt{0.8936}\approx0.95
$$

# Answer:
0.95

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Question

Explanation:

Step1: Calculate the expected value \(E(X)\)

Step2: Calculate \(E(X^{2})\)

Step3: Calculate the variance \(\text{Var}(X)\)

Step4: Calculate the standard deviation \(\sigma\)

Answer: