the movie critic liked to count the number of actors in each movie she saw.
|number of actors|number of movies|
|----|----|
|45|3|
|54|2|
|56|1|
|68|1|
|84|1|
|91|2|
x is the number of actors that a randomly chosen movie had. what is the standard deviation of x?
round your answer to the nearest hundredth.

Question

Accepted Answer

# Explanation:
## Step1: Calculate the total number of movies
$3 + 2+1 + 1+1 + 2=10$
## Step2: Calculate the expected - value (mean) $\mu$
$$
\begin{align*}
\mu&=\frac{45\times3 + 54\times2+56\times1 + 68\times1+84\times1 + 91\times2}{10}\
&=\frac{135+108 + 56+68+84+182}{10}\
&=\frac{633}{10}=63.3
\end{align*}
$$
## Step3: Calculate the variance $\sigma^{2}$
$$
\begin{align*}
\sigma^{2}&=\frac{3\times(45 - 63.3)^{2}+2\times(54 - 63.3)^{2}+1\times(56 - 63.3)^{2}+1\times(68 - 63.3)^{2}+1\times(84 - 63.3)^{2}+2\times(91 - 63.3)^{2}}{10}\
&=\frac{3\times(- 18.3)^{2}+2\times(-9.3)^{2}+1\times(-7.3)^{2}+1\times(4.7)^{2}+1\times(20.7)^{2}+2\times(27.7)^{2}}{10}\
&=\frac{3\times334.89+2\times86.49+1\times53.29+1\times22.09+1\times428.49+2\times767.29}{10}\
&=\frac{1004.67+172.98+53.29+22.09+428.49+1534.58}{10}\
&=\frac{3216.1}{10}=321.61
\end{align*}
$$
## Step4: Calculate the standard - deviation $\sigma$
$\sigma=\sqrt{321.61}\approx17.93$
# Answer:
$17.93$

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QUESTION IMAGE

Question

Explanation:

Step1: Calculate the total number of movies

Step2: Calculate the expected - value (mean) $\mu$

Step3: Calculate the variance $\sigma^{2}$

Step4: Calculate the standard - deviation $\sigma$

Answer: