Question

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 0.22 0.16 0.03 0.02 0.02 0.01 0.01 (a) Compute the mean, variance and standard deviation (accurate to one decimal place). mean variance standard deviation (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 the largest (whole) number of video arcades you should install so as to comply with this regulation? arcades

Answer 1

Excel calculations

X	P(X=x)	xP(x)	x^2P(x)
0	0.07	0	0
1	0.09	0.09	0.09
2	0.37	0.74	1.48
3	0.22	0.66	1.98
4	0.16	0.64	2.56
5	0.03	0.15	0.75
6	0.02	0.12	0.72
7	0.02	0.14	0.98
8	0.01	0.08	0.64
9	0.01	0.09	0.81
		2.71	10.01
Mean	2.71
Variance	2.6659
stdev	1.632758