Your company, Sonic Video, Inc., has conducted research that shows the probability distribution, where X is the number of video arcades in a randomly chosen city with more than 500,000 inhabitants.

x	0	1	2	3	4	5	6	7	8	9
P(X = x)	0.07	0.09	0.37	0.23	0.15	0.03	0.02	0.02	0.01	0.01

(a) Compute the mean, variance and standard deviation (accurate to one decimal place).

(b) 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% of all cities. What is this range? (Find the interval containing at least 3/4 of the data as guaranteed by Chebyshev's Rule. Round your answers to one decimal place.)

,

What is thelargest(whole) number of video arcades you should install so as to comply with this regulation?