Your Company, Sonic Video, Inc ​
Compute the Mean $\mu =$

Your company, Sonic Video, Inc., has conducted research that shows the following probability distribution, where X is the number of video arcades in a randomly chosen city with more than 500,000 inhabitants. $$\begin{array} { | c | c | c | c | c | c | c | c | c | c | c | } \hline x & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 \\\hline P ( X = x ) & 0.05 & 0.11 & 0.34 & 0.24 & 0.14 & 0.06 & 0.02 & 0.02 & 0.01 & 0.01 \\\hline\end{array}$$ ​
Compute the mean. Please round your answer to one decimal place. $\mu =$ __________
Compute the variance. Use the rounded value for the mean in your calculations. Round your answer to one decimal place. $\sigma ^ { 2 } =$ __________
Compute the standard deviation. Use the rounded value for the variance in your calculations. Round your answer to one decimal place. $\sigma =$ __________
As CEO of Startrooper Video Unlimited, you wish to install a chain of video arcades in Sleepy City, U.S.A. The city council regulations require that the number of arcades be within the range shared by at least 75 percent of all cities. Find this range. Please round your answers to one decimal place.
from __________ to __________
Find the largest number of video arcades you should install so as to comply with this regulation.
The largest number is __________.